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‘

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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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********************************************** 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 

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***************************************************************  FSc  BSc  MSc / BS  MPhil / MS  PhD  Old Papers / Entry Test

o Check out all these at 

http://www.MathCity.org

***************************************************************

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