Talk:Metabelian group

Metabelian groups and "residually abelian" groups

Hi, I'm wondering if residually abelian would be the same or related to metabelian. For all I know, residually abelian might actually imply abelian. Thanks, Richard Peterson198.189.194.129 (talk) 23:25, 14 March 2012 (UTC)

Residually abelian is the same as abelian. --Zundark (talk) 09:14, 15 March 2012 (UTC)

thanks would you care to say why?198.189.194.129 (talk) 00:28, 16 March 2012 (UTC)

If you look at the definition of residually X, in the case where X is "abelian" it essentially says "every non-identity element lies outside the derived subgroup" - i.e., the derived subgroup is trivial. --Zundark (talk) 12:46, 16 March 2012 (UTC)