Talk:Residually finite group

From Wikipedia, the free encyclopedia

Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	Stub Class	Low Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 23:09, 10 July 2007 (UTC)

[edit] Unsourced (nontrivial?) theorem

An equivalent definition is that a group is residually finite if the intersection of all its finite index subgroups is trivial.

Er, really? Without thinking about this, at all, it is quite obvious that a group is RF if the intersection of all its finite index normal subgroups is trivial. Can someone provide a proof for the other equivalence?

RandomP 14:45, 22 September 2006 (UTC)

Probably an error? I changed it to "normal", which generally occurs in the definition of "residually something". - Momotaro 14:00, 21 February 2007 (UTC)

It wasn't an error: in any group, the intersection of all subgroups of finite index is the same as the intersection of all normal subgroups of finite index. (By the way, the merge tags you added have been there for more than a month, and nobody has disagreed, so I suggest we go ahead and merge. The merged article should be at residually finite group.) --Zundark 07:57, 3 April 2007 (UTC)