Groups Handwritten Notes
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Groups: Handwritten notes by Atiq ur Rehman http://www.MathCity.org/atiq Partial Contents 1. Groups; definition and examples 1 2. Order of group, order of element 3 3. Periodic group, mixed group 4 4. Subgroup 6 5. Invalution 8 6. Relation between groups, homomorphism, monomorphism, epimorphism, isomorphism, endomorphism, examples and related theorem 9 7. Kernel, definition and related theorems 13 8. Cyclic group, related theorems 18 9. Complex in a group, product of complexes and related theorems 24 10. Coset, definition and examples 30 11. Index of subgroup, Lagrange’s theorem 31 12. Double coset, related theorem 33 13. Normalizer, definition and related theorems 34 14. Centralizer, centre of group, related theorem 36 15. Conjugate or transform of a group, definition and related theorems 37 a
16. Self conjugate, conjugancy class, related theorem 40 17. Class equation, p-group, definition and related theorems 43 18. Conjugate subgroup, definition and related theorems 45 19. Normal subgroup, definition and related theorems 49 20. Factor or quotient group, definition and related theorem 53 21. 1st isomorphism theorem, related theorem 55 22. 2nd isomorphism theorem 58 23. 3rd isomorphism theorem 60 24. Endomorphism, automorphism, definition and related theorem 62 25. Conjugation as an automorphism 64 26. Inner and outer automorphism, definition and related theorems 65 27. Commutator of a group, definition and related theorem 70 28. Derive group or commutative group, definition and related theorem 71 29. Direct product of groups, definition and related theorems 73 30. Invariant subgroup 79 31. Characteristic subgroup 80‘
Available at http://www.MathCity.org/msc If you have any question, ask at http://forum.mathcity.org MathCity.org is a non-profit organization, working to promote mathematics in Pakistan. If you have anything (notes, model paper, old paper etc.) to share with other peoples, you can send us to publish on MathCity.org. You may earn money by participating. For more information visit: http://www.MathCity.org/participate.html b
Groups (Handwritten notes)
MathCity.org
Written by: Atiq ur Rehman, Rehman, Class: BS or MSc (Maths)
Merging man and maths
Available online at http://www.MathCity.org , Version: 1.0.0
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Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org **********************************************
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www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
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Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
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www.MathCity.org
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www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
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********************************************** Available online at http://www.MathCity.org **********************************************
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********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
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www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org ********************************************** Discuss your problems at
http://forum.mathcity.org
******************************************
[56]
www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org ********************************************** [57]
Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
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www.MathCity.org
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Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
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www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
*************************************************************** FSc BSc MSc / BS MPhil / MS PhD Old Papers / Entry Test
o Check out all these at
http://www.MathCity.org
***************************************************************
[66]
www.MathCity.org
[67]
Groups: Handwritten notes
www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org ********************************************** Ask questions at http://forum.mathcity.org ********************************************** *************************************************************** FSc BSc MSc / BS MPhil / MS PhD Old Papers / Entry Test
o Check out all these at
http://www.MathCity.org
*************************************************************** [68]
www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
***************************************************** Check out notes of other subjects at http://www.MathCity.org *****************************************************
[72]
www.MathCity.org
[73]
Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
[74]
www.MathCity.org
Groups: Handwritten notes
*************************************************************** FSc BSc MSc / BS MPhil / MS PhD Old Papers / Entry Test
o Check out all these at
http://www.MathCity.org
***************************************************************
[75]
Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
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16. Self conjugate, conjugancy class, related theorem 40 17. Class equation, p-group, definition and related theorems 43 18. Conjugate subgroup, definition and related theorems 45 19. Normal subgroup, definition and related theorems 49 20. Factor or quotient group, definition and related theorem 53 21. 1st isomorphism theorem, related theorem 55 22. 2nd isomorphism theorem 58 23. 3rd isomorphism theorem 60 24. Endomorphism, automorphism, definition and related theorem 62 25. Conjugation as an automorphism 64 26. Inner and outer automorphism, definition and related theorems 65 27. Commutator of a group, definition and related theorem 70 28. Derive group or commutative group, definition and related theorem 71 29. Direct product of groups, definition and related theorems 73 30. Invariant subgroup 79 31. Characteristic subgroup 80‘
Available at http://www.MathCity.org/msc If you have any question, ask at http://forum.mathcity.org MathCity.org is a non-profit organization, working to promote mathematics in Pakistan. If you have anything (notes, model paper, old paper etc.) to share with other peoples, you can send us to publish on MathCity.org. You may earn money by participating. For more information visit: http://www.MathCity.org/participate.html b
Groups (Handwritten notes)
MathCity.org
Written by: Atiq ur Rehman, Rehman, Class: BS or MSc (Maths)
Merging man and maths
Available online at http://www.MathCity.org , Version: 1.0.0
[1]
Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org **********************************************
[2]
www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
[3]
Groups: Handwritten notes
www.MathCity.org
[4]
www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
[5]
Groups: Handwritten notes
www.MathCity.org
[6]
www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
[7]
Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org **********************************************
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www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org **********************************************
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www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org **********************************************
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www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org **********************************************
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www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org **********************************************
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www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
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Groups: Handwritten notes
www.MathCity.org
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Groups: Handwritten notes
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Groups: Handwritten notes
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www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
[55]
Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
********************************************** Available online at http://www.MathCity.org ********************************************** Discuss your problems at
http://forum.mathcity.org
******************************************
[56]
www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org ********************************************** [57]
Groups: Handwritten notes
www.MathCity.org
[58]
www.MathCity.org
[59]
Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
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Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
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www.MathCity.org
[65]
Groups: Handwritten notes
www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org **********************************************
*************************************************************** FSc BSc MSc / BS MPhil / MS PhD Old Papers / Entry Test
o Check out all these at
http://www.MathCity.org
***************************************************************
[66]
www.MathCity.org
[67]
Groups: Handwritten notes
www.MathCity.org
Groups: Handwritten notes
********************************************** Available online at http://www.MathCity.org ********************************************** Ask questions at http://forum.mathcity.org ********************************************** *************************************************************** FSc BSc MSc / BS MPhil / MS PhD Old Papers / Entry Test
o Check out all these at
http://www.MathCity.org
*************************************************************** [68]
www.MathCity.org
[69]
Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
[70]
www.MathCity.org
[71]
Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
***************************************************** Check out notes of other subjects at http://www.MathCity.org *****************************************************
[72]
www.MathCity.org
[73]
Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
[74]
www.MathCity.org
Groups: Handwritten notes
*************************************************************** FSc BSc MSc / BS MPhil / MS PhD Old Papers / Entry Test
o Check out all these at
http://www.MathCity.org
***************************************************************
[75]
Groups: Handwritten notes
www.MathCity.org
[76]
www.MathCity.org
[77]
Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
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Groups: Handwritten notes
Groups: Handwritten notes
www.MathCity.org
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