Timeline for Defining an Arbitrary Group
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 14, 2020 at 19:14 | answer | added | AmirHosein Sadeghimanesh | timeline score: 2 | |
| Feb 14, 2018 at 16:58 | comment | added | David G. Stork | Create a matrix the describes the multiplication table for the group. | |
| Feb 14, 2018 at 9:09 | comment | added | yarchik | Your question about infinite groups goes beyond the scope of this site. MA has no build-in capabilities to deal with them. However, it is possible to study infinite group families, e.g. cyclic groups and their direct products. Concerning your original question about defining the multiplication table for a set of elements---the binary operation. It is pretty inefficient way to define the group. Rather, one should consider a set of generators and relations among them: mathematica.stackexchange.com/questions/96111/… | |
| Feb 14, 2018 at 7:54 | comment | added | b3m2a1 | @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. | |
| Feb 14, 2018 at 6:47 | history | edited | Brandon Myers | CC BY-SA 3.0 | added 1 character in body |
| Feb 14, 2018 at 6:47 | comment | added | Brandon Myers | @yarchik what about arbitrary infinite groups? | |
| Feb 14, 2018 at 6:46 | comment | added | Brandon Myers | @David G. Stork, could you clarify what you mean by this? | |
| Feb 13, 2018 at 8:30 | comment | added | yarchik | It is the Cayley's theorem that every finite group can be represented as a group of permutations. | |
| Feb 13, 2018 at 5:52 | comment | added | David G. Stork | Define the multiplication table. | |
| Feb 13, 2018 at 5:50 | history | asked | Brandon Myers | CC BY-SA 3.0 |