Robin Chapman <firstname.lastname@example.org> wrote in message news:<email@example.com>... >> A known theorem of Schur states that if in a group G >> the index of the center Z(G) is finite then the derived > >You mean "centre"? >
Whichever you prefer.
>> subgroup [G,G] is also finite. Does the converse of >> this statement hold as well? > >You mean >"If [G,G] is finite, then is |G:Z(G)| finite?" ?
Yes, this is what I mean.
>What if G is an infinite Abelian group?
In this case the order of [G,G] is 1 and so is the index |G:Z(G)|. Was it meant to be a counterexample?