Book on finite group theory, containing a sufficient number of examples

Question

I read M.Isaacs book on finite group theory now and I find it quite interesting and well written. But also I feel that there are not enough examples (for me) in this book.

Maybe there is another book wich can be used to complement Isaacs book which contain enough examples? Or maybe there are resources, where one can find interesting and demonstrative examples concerning finite groups?

See if this helps you: https://math.stackexchange.com/questions/25506/introductory-group-theory-textbook — , Jan 04 '18 at 10:05
Last year Serre just wrote a new book on finite groups, he's one of the best writer in mathematics. The two last chapters are about finite subgroup of $\rm{GL}_n$ and group of small order. — Nicolas Hemelsoet, Jan 04 '18 at 10:31
I agree with @NicolasHemelsoet that it's always worth checking out Serre. The specific book is Serre - Finite groups: An introduction, also sold through the AMS. There is an MAA review, which suggests that it may not be at the level for someone looking for an introduction to group theory. (I cannot tell whether that describes the poster.) — LSpice, Jan 04 '18 at 17:14

Nicky Hekster · Accepted Answer · 2018-01-04T17:53:22.777

6

Why not try one of the following:

John S. Rose, A Course on Group Theory

Derek J.S. Robinson, A Course in The Theory of Groups

Dummit and Foote, Abstract Algebra.

Each of these books has a lot of good examples and exercises!

edited Jan 04 '18 at 17:53

answered Jan 04 '18 at 14:22

Nicky Hekster

52,147

2

Second the vote for Dummitt & Foote (+1). It covers a lot more than finite groups, but is really an example-based text that is also very rigorous. Highly recommend. – rogerl Jan 04 '18 at 15:00
Thank you, Nicky. I knew about the DF book, but somehow underestimated it. But in DF book there are no such deep topics as in Isaacs book (for example Chermak-Delgado measure) and so less or more non-trivial examples one forced to look elsewhere. – Mikhail Goltvanitsa Jan 04 '18 at 16:07
It's too small to try suggesting the edit, but, as @rogerl politely points out, you probably want to change the spelling of 'Foote' (from 'Foot'). – LSpice Jan 04 '18 at 17:24
1

@Lspice, Certainly a "misstep" :-) Thanks for pointing out. – Nicky Hekster Jan 04 '18 at 17:53
@NickyHekster, well, I guess I put Foote in your mouth. ;-) – LSpice Jan 04 '18 at 17:56

score 4 · Answer 2 · answered Jan 04 '18 at 10:23

Groups: A Path to Geometry by R.P. Burn is an introduction to group theory that consists entirely of examples, problems and solutions.

Schaum's Outline of Group Theory by B. Baumslag contains lots of examples and problems with solutions.

Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys by David Joyner is built around a series of concrete examples and applications of groups.

score 4 · Answer 3 · answered Jan 04 '18 at 17:11

4

A very literal answer: Michael Weinstein has a book called Examples of groups.

answered Jan 04 '18 at 17:11

LSpice

2,891

Thank you, I never hear about this book. – Mikhail Goltvanitsa Jan 04 '18 at 20:16

score 1 · Answer 4 · answered Jan 05 '18 at 02:32

I prefer, the following books for group theory in order.

Abstract Algebra by "Dummit & Foote", Wiley publication.
A course in Abstract Algebra By, "khanna and Bhambri", vikas publication.
Contemporary Abstract Algebra By "Gallian".

If you want, classic text with lots of examples prefer, (1) and (3) and if you want lots of solved examples prefer (2). In (2) there are lots of solved examples, covering all topics, groups, rings, fields, In fact on linear transformations too.

Thank you, Akash! Despite the third book seems to be elementary, there is a quite useful section suggested readings! — Mikhail Goltvanitsa, Jan 05 '18 at 07:51

Book on finite group theory, containing a sufficient number of examples

4 Answers4