Fundamentals of Group Theory: An Advanced Approach

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<div style="MARGIN: 0in 0in 0pt"><em><span style="COLOR: black">Fundamentals of Group Theory </span></em><span style="COLOR: black">provides a comprehensive account of the basic theory of groups. Both classic and unique topics in the field are covered, such as an historical look at how Galois viewed groups, a discussion of commutator and Sylow subgroups, and a presentation of Birkhoff’s theorem. Written in a clear and accessible style, the work presents a solid introduction for students wishing to learn more about this widely applicable subject area. </span></div>
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<div style="MARGIN: 0in 0in 0pt"><span style="COLOR: black">This book will be suitable for graduate courses in group theory and abstract algebra, and will also have appeal to advanced undergraduates. In addition it will serve as a valuable resource for those pursuing independent study. <em>Group Theory </em>is a timely and fundamental addition to literature in the study of groups. </span></div>

Author(s): Steven Roman (auth.)
Edition: 1
Publisher: Birkhäuser Basel
Year: 2012

Language: English
Pages: 380
Tags: Group Theory and Generalizations; Algebra; Order, Lattices, Ordered Algebraic Structures

Front Matter....Pages i-xii
Preliminaries....Pages 1-17
Groups and Subgroups....Pages 19-60
Cosets, Index and Normal Subgroups....Pages 61-103
Homomorphisms, Chain Conditions and Subnormality....Pages 105-148
Direct and Semidirect Products....Pages 149-190
Permutation Groups....Pages 191-206
Group Actions; The Structure of P -Groups....Pages 207-233
Sylow Theory....Pages 235-262
The Classification Problem for Groups....Pages 263-271
Finiteness Conditions....Pages 273-289
Solvable and Nilpotent Groups....Pages 291-317
Free Groups and Presentations....Pages 319-352
Abelian Groups....Pages 353-365
Back Matter....Pages 367-380