Ayache A., Amin K. Introduction to Group Theory 2025

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Ayache A., Amin K. Introduction to Group Theory 2025

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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