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I need good texts on group theory that cover the theory of permutation groups. I think there is a book called Wielandt. Is it good? are there newer alternatives? Can I find books that are not specifically about representation groups that cover thoroughly the most important results? Also, when browsing Amazon I kept getting sent to books on representation theory of finite groups, would this be a good way to approach the topic? I got interested in the topic thanks to this question I asked recently.

Thank you very much in advance.

Regards.

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  • $\begingroup$ you can always start with knuth's volume 4a. $\endgroup$ – abel Jan 5 '15 at 5:30
  • $\begingroup$ @M.Vinay, not abstract permutation groups. if you are looking for abstract/pure permutations groups then there is wielandt or sagan that i know of. $\endgroup$ – abel Jan 5 '15 at 5:37
  • $\begingroup$ @abel I found a PDF online (cs.utsa.edu/~wagner/knuth/fasc2b.pdf) and it does have some group theory (definition of group of permutations, and Cayley graphs), but focuses on algorithmic aspects. It doesn't have anything on more group theoretic topics such as subgroups and automorphisms. $\endgroup$ – M. Vinay Jan 5 '15 at 5:41
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You might appreciate Sagan's book The symmetric group; it covers, well, its namesake. It is largely focused on the representation theory of $S_n$, but covers other topics as well.

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Wielandt's book is quite old now, but still good. If you are looking for more recent books, at the beginning postgraduate level, then there is "Permutation groups" by Peter J. Cameron, and (believe it or not) "Permutation groups" by J.D. Dixon abnd B. Mortimer.

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  • $\begingroup$ I was just going to suggest Dixon. I came across this in a citation on an algebraic graph theory paper! $\endgroup$ – ml0105 Jan 6 '15 at 5:18
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A very good book is Donald S. Passman, Permutation Groups. And yes, Helmut Wielandt's book Finite Permutation Groups.

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