Description
This book can also serve as a reference for professional mathematicians. The book contains 221 carefully selected exercises of varying difficulty which will allow students to practice their own computational and proof-writing skills. Sample solutions to some exercise questions are provided, from which students can learn to write their own solutions and proofs. Besides standard ones, many of the exercises are very interesting.
Group Theory includes:
- basic properties of groups
- symmetric groups and alternating groups
- isomorphism theorems, commutator subgroups, direct and semi-direct products of groups
- group action on sets, Cauchy-Frobenius Lemma, symmetries of the regular polyhedrons
- Jordan-Holder Theorem and Sylow Theorems
- free groups, group presentations, finitely generated abelian groups
- solvable groups, Hall subgroups, characteristically simple groups, Sylow systems and Sylow bases
- nilpotent groups, Frattini subgroups
- basic properties of representations of groups on vector spaces, subrepresentations; irreducibility, Schur's Lemma, and Maschke's Theorem
Book Information
ISBN 9781792478925
Author Kaiming Zhao
Format Paperback
Page Count 277
Imprint Kendall/Hunt Publishing Co ,U.S.
Publisher Kendall/Hunt Publishing Co ,U.S.