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April 20, 2026, 10:27 p.m.
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SOURCE: Ayache A., Amin K. Introduction to Group Theory 2025
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COVER
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MEDIAINFO
Textbook in PDF format
Targeted at undergraduate mathematics students, this book aims to cover courses in group theory. Based on lectures in group theory, it includes many illustrations and examples, numerous solved exercises and detailed proofs of theorems. The book acts as a guide to teachers and is also useful to graduate students. The book discusses major topics in group theory such as groups and subgroups, binary operations, fundamental algebraic structure of groups, symmetric groups, cyclic groups, normal subgroups, quotient groups, homomorphisms, isomorphisms, direct product of groups, simple groups, set on a group, Sylow's theorem, finite group, Abelian groups and non-isomorphic Abelian groups.
Preface
Notations and Symbols
Groups and Subgroups
Binary Operations
Groups
Subgroups
Permutation Groups
Cyclic Groups
Normal Subgroups
Cosets and Lagrange's Theorem
Normal Subgroups and Quotient Groups
Homomorphisms
Isomorphism Theorems
Direct Product of Groups
Simple Groups
Finite Groups
Group Action
Sylow's Theorems
Finite Abelian Groups
Series Groups
Derived Groups
Solvable Groups
Composition Series
Nilpotent Groups
Appendix Answers and Comments
Appendix References
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