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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MathCity.org Merging man and maths
Groups (Handwritten notes) Written by: Atiq ur ReWritten by: Atiq ur ReWritten by: Atiq ur ReWritten by: Atiq ur Rehman, Class: BS or MSc (Maths)hman, Class: BS or MSc (Maths)hman, Class: BS or MSc (Maths)hman, 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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Available online at http://www.MathCity.org
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Discuss your problems at http://forum.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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� FSc
� BSc
� MSc / BS
� MPhil / MS
� PhD
� Old Papers / Entry Test
o Check out all these at
� http://www.MathCity.org
***************************************************************
www.MathCity.org
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Groups: Handwritten notes
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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
***************************************************************
www.MathCity.org
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Groups: Handwritten notes
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www.MathCity.org
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Check out notes of other subjects at http://www.MathCity.org
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Groups: Handwritten notes
www.MathCity.org
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Groups: Handwritten notes
www.MathCity.org
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Groups: Handwritten notes
***************************************************************
� FSc
� BSc
� MSc / BS
� MPhil / MS
� PhD
� Old Papers / Entry Test
o Check out all these at
� http://www.MathCity.org
***************************************************************
www.MathCity.org
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={ The End }=
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