I learned today, while doing my homework, that Mathematica can understand group theory. Combing through the documentation though just gave the examples of permutation groups. I would like to know how to define an arbitrary group, some set and a binary operation on that set. Ideally, this would allow the use of the other built-in functions such as those for finding the order of a group or element, etc.

  • $\begingroup$ Define the multiplication table. $\endgroup$ – David G. Stork Feb 13 '18 at 5:52
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    $\begingroup$ It is the Cayley's theorem that every finite group can be represented as a group of permutations. $\endgroup$ – yarchik Feb 13 '18 at 8:30
  • $\begingroup$ @David G. Stork, could you clarify what you mean by this? $\endgroup$ – Brandon Myers Feb 14 '18 at 6:46
  • $\begingroup$ @yarchik what about arbitrary infinite groups? $\endgroup$ – Brandon Myers Feb 14 '18 at 6:47
  • $\begingroup$ @BrandonMyers In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group acting on G. All groups are included. Note though that it also says: Nevertheless, Alperin and Bell note that "in general the fact that finite groups are imbedded in symmetric groups has not influenced the methods used to study finite groups" Note, too, while representing a group is trivial, doing things with it isn't. If you have a specific target it will be easier to help. $\endgroup$ – b3m2a1 Feb 14 '18 at 7:54

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