Groups Handwritten Notes

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A handwritten notes of groups, usually teaches in universities of Pakistan. Best to prepare a Group section of Algebra paper in MSc.

Text of Groups Handwritten Notes

Groups: Handwritten notes by Atiq ur Rehman http://www.MathCity.org/atiq Partial Contents1. Groups; denition 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, denition and related theorems 13 8. Cyclic group, related theorems 18 9. Complex in a group, product of complexes and related theorems 24 10. Coset, denition and examples 30 11. Index of subgroup, Lagranges theorem 31 12. Double coset, related theorem 33 13. Normalizer, denition and related theorems 34 14. Centralizer, centre of group, related theorem 36 15. Conjugate or transform of a group, denition and related theorems 37 a

16. Self conjugate, conjugancy class, related theorem 40 17. Class equation, p-group, denition and related theorems 43 18. Conjugate subgroup, denition and related theorems 45 19. Normal subgroup, denition and related theorems 49 20. Factor or quotient group, denition and related theorem 53 21. 1st isomorphism theorem, related theorem 55 22. 2nd isomorphism theorem 58 23. 3rd isomorphism theorem 60 24. Endomorphism, automorphism, denition and related theorem 62 25. Conjugation as an automorphism 64 26. Inner and outer automorphism, denition and related theorems 65 27. Commutator of a group, denition and related theorem 70 28. Derive group or commutative group, denition and related theorem 71 29. Direct product of groups, denition and related theorems 73 30. Invariant subgroup 79 31. Characteristic subgroup 80

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Groups (Handwritten notes)Rehman, Written by: Atiq ur Rehman, Class: BS or MSc (Maths)Available online at http://www.MathCity.org , Version: 1.0.0

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Groups: Handwritten notes

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********************************************** Available online at http://www.MathCity.org **********************************************

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