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My education on groups is by far and away deficient but one of the better books I came across is called "Fundamental Algorithms for Permutation Groups" by G. Bu
by abetusk 5y ago
My education on groups is by far and away deficient but one of the better books I came across is called "Fundamental Algorithms for Permutation Groups" by G. Butler [0]. It's kind of old (1991) but, in my opinion, excellent, especially for some one like me that's concerned with computation, run-time, algorithms, etc.
There's also a Akos Seress book, "Permutation Group Algorithms", which fills in some mathematical details and proofs but, notably, doesn't have one line of pseudo-code in the book.
Both focus on algorithms, and permutation groups in particular, which is just a small subset of group theory.
[0] https://www.springer.com/gp/book/9783540549550 https://www.springer.com/gp/book/9783540549550
- sdenton4 5y agoFor the permutation group in particular, it's hard to beat Sagan's 'The Symmetric Group.' It's a bit more recent, and covers lots of really beautiful topics, and really shows off the nice connections between the combinatorics of S_n and the representation theory. https://www.springer.com/gp/book/9780387950679 https://www.springer.com/gp/book/9780387950679
- abetusk 5y agoThanks for the recommendation. Just briefly reviewing it, this is the kind of book I tend to shy away from. I'm sure it's a good reference for a particular type of group theory but I doubt I would use this type of book for anything but a reference. I can't find any mention of "strong generating set" or algorithmic considerations of how to actually compute with permutation groups. As with many of the Springer books, it feels like a collection of scattered knowledge without a cohesive narrative. It's completely possible I'm missing something with this book, especially since I haven't read it, and that for more mathematically minded folks, this book is a better introduction.