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)