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Lecture Notes |
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Authors: |
Atiq ur Rehman |
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Hardcover: |
82 pages |
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Language: |
English (Handwritten) |
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Format: |
PDF & DjVu (See
Download
section for PDF or DjVu Viewer) |
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Size: |
PDF: 4.48MB, DjVu: 3.56MB
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CONTENTS OR SUMMARY: |
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◊ Groups; definition and examples
◊ Order of group, order of element
◊ Periodic group, mixed group
◊ Subgroup
◊ Invalution
◊ Relation between groups, homomorphism, monomorphism,
epimorphism, isomorphism, endomorphism, examples and related
theorem
◊ Kernel, definition and related theorems
◊ Cyclic group, related theorems
◊ Complex in a group, product of complexes and related
theorems
◊ Coset, definition and examples
◊ Index of subgroup, Lagrange's theorem
◊ Double coset, related theorem
◊ Normalizer, definition and related theorems
◊ Centralizer, centre of group, related theorem
◊ Conjugate or transform of a group, definition and
related theorems
◊ Self conjugate, conjugancy class, related theorem
◊ Class equation, p-group, definition and related
theorems
◊ Conjugate subgroup, definition and related theorems
◊ Normal subgroup, definition and related theorems
◊ Factor or quotient group, definition and related
theorem
◊ 1st isomorphism theorem, related theorem
◊ 2nd isomorphism theorem
◊ 3rd isomorphism theorem
◊ Endomorphism, automorphism, definition and related
theorem
◊ Conjugation as an automorphism
◊ Inner and outer automorphism, definition and related
theorems
◊ Commutator of a group, definition and related
theorem
◊ Derive group or commutative group, definition and
related theorem
◊ Direct product of groups, definition and related
theorems
◊ Invariant subgroup
◊ Characteristic subgroup
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