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Can you suggest me a book in abstract algebra that has good exercises specific to group actions and Sylow's theorems ? I have the book A First Course in Abstract Algebra by Fraleigh, but it doesn't have a lot of exercises on these topics.

J. W. Tanner
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領域展開
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    Milne's group theory notes have a lot of exercises in these topics. – George Giapitzakis Jul 09 '21 at 13:11
  • @GiorgosGiapitzakis thanks, I am gonna check it out. – 領域展開 Jul 09 '21 at 13:18
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    None of these posts answer my question, my question was very specific, anyway. – 領域展開 Jul 09 '21 at 13:39
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    @PetrosK And yet, with one small exception, all four posts recommend exactly the two books which you got in answer to your question below. One begins to wonder exactly how many different ways the question needs to be asked when the answers are all the same. At least two of them specifically discuss resources for group actions and Sylow theorems. Really, you just need good introductory references: they are all bound to have exercises and examples you want. There is no "magic exercise and examples book" that someone is going to recommend. – rschwieb Jul 09 '21 at 13:46
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    I slightly disagree most books are very bad and with no suited exercises, my post has been associated with other 4 post with at least 6 answers on every one, which means I must look roughly 24 books to see what suits for me – 領域展開 Jul 09 '21 at 14:48
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    @PetrosK Now now, it is hardly that onerous. Yes, you might read at most 24 answers (not books) and if you can’t be bothered to look for answers first you will probably have a lot of questions closed as duplicates. Secondly, a lot of the answers concur about various recommendations, and go into detail about why they’re good and what they have. You are not the first person to value examples and exercises (shocking, eh?) and you will find many people value make recommendations based on that. So the actual number of books to check is far less, maybe more like 5 that sound about right. – rschwieb Jul 09 '21 at 17:03
  • Petros, assuming you can read French, have a look at Chapter 1 of Perrin's Cours d'algèbre. – Anonymous Aug 23 '21 at 16:18

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I suggest two books:

  1. Abstract Algebra by David S. Dummit and Richard M. Foote
  2. Contemporary Abstract Algebra by Joseph A. Gallian

The first book has a chapter on group actions which contains Sylow's theorem with a set of good problems. The second book has a dedicated chapter on Sylow's theorem and a lot of problems also.

Infinity_hunter
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