Wikipedia:Reference desk/Archives/Mathematics/2018 October 22
| Mathematics desk | ||
|---|---|---|
| < October 21 | << Sep | October | Nov >> | Current desk > |
| Welcome to the Wikipedia Mathematics Reference Desk Archives |
|---|
| The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
October 22
[edit]Infinite group containing all finite groups
[edit]Does there exist an infinite group that contains an isomorphic copy of every finite group? Can the isomorphic copies all be normal subgroups? GeoffreyT2000 (talk) 16:02, 22 October 2018 (UTC)
- Yes, just take the product of one copy of each isomorphism type of finite group. Edit: This example is uncountable, but you can even find one which is countable. –Deacon Vorbis (carbon • videos) 16:24, 22 October 2018 (UTC)