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I almost got a Math degree but want to learn better topics in group theory, expecially about finite ones. I studied just introductions on groups (in the firsts algebra courses) and something about group actions and theory of characters. Could anyone recommend a good book on the topic? Thank you

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    $\begingroup$ Bertram Huppert's Endliche Gruppen may be suitable for you to learn finite groups. This book covers many topics in finite groups thoroughly, but is also a bit too long if you want to learn in a short period. $\endgroup$ – josephz Oct 31 '17 at 1:50
  • $\begingroup$ Thanks, I'm going to check the index. $\endgroup$ – Tancredi Oct 31 '17 at 2:03
  • $\begingroup$ Introduction to the Theory of Finite Groups by Walter Ledermann. $\endgroup$ – bof Oct 31 '17 at 8:39
  • $\begingroup$ Rotman's Introduction to Finite Groups is really great. $\endgroup$ – Pedro Tamaroff Oct 31 '17 at 11:22
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Elements of Abstract Algebra by Allan Clark
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Theory of Groups of Finite Order by William Burnside
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A Course on Group Theory by H.E. Rose
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In German Edition:
Endliche Gruppen I and II by Bertram Huppert
Algebra: Gruppen - Ringe - Körper by Karpfinger

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    $\begingroup$ I think the book by Burnside is a terrible suggestion. It is simply too old to be useful for anyone who actually wants to learn group theory. It is a nice thing to read for the history, but way too much has happened to the way we think about these things for the actual material to be a good starting point for anyone now. $\endgroup$ – Tobias Kildetoft Oct 31 '17 at 9:01
  • $\begingroup$ Thanks for the suggestions $\endgroup$ – Tancredi Oct 31 '17 at 17:04
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For the representation theory of finite groups, I suggest Serre's Linear Representations of Finite Groups.

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Contemporary Abstract Algebra by Joseph A Gallian

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As already mentioned, Gallian's Contemporary Abstract Algebra is a good place to start. I also really like Dummit and Foote's Abstract Algebra, though this is primarily a first year graduate text, so it may be a bit terse in some places.

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