Wikipedia:Reference desk/Archives/Mathematics/2018 October 22
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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)