The most effective way to study any branch of mathematics is to tackle its problems. This wide-ranging anthology offers a straightforward approach, with 431 challenging problems in all phases of group theory, from elementary to the most advanced.
The problems are arranged in eleven chapters: subgroups, permutation groups, automorphisms and finitely generated Abelian groups, normal series, commutators and derived series, solvable and nilpotent groups, the group ring and monomial representations, Frattini subgroup, factorization, linear groups, and representations and characters. Each chapter features a preface of pertinent definitions and theorems, and full solutions appear in a separate section.
Most of these problems are derived from research papers published since 1950 (a listing of 102 references is supplied). This compilation makes them readily accessible as a supplement to courses in group theory. The presentation places equal emphasis on techniques and results, encouraging the development of both skill and comprehension.
Table of ContentsList of Symbols; Introduction
1. Subgroups. Problems. Solutions
2. Permutation Groups. Problems. Solutions
3. Automorphisms and Finitely Generated Abelian Groups. Problems. Solutions
4. Normal Series. Problems. Solutions
5. Commutators and Derived Series. Problems. Solutions
6. Solvable and Nilpotent Groups. Problems. Solutions
7. The Group Ring and Monomial Representations.. Problems. Solutions
8. Frattini Subgroup. Problems. Solutions
9. Factorization. Problems. Solutions
10. Linear Groups. Problems. Solutions
11. Representations and Characters. Problems. Solutions
References; Index of Terms
Most Helpful Customer Reviews
Found this little book almost 12 years ago when I was a grad student. I still do problems from this book!! The solutions are clear, and most people will easily supply the missing details (the ideas for the missing details are always given). A true jewel in group theory.
this book is a great supplemental reading for anyone taking a course in group theory. There are many problems that occur in many textbooks; solutions are in most cases easy to follow; in some cases the reader will need to fill in the details. In any case, this a very helpful reference book.