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Anvita
Posts:
29
Registered:
12/13/04


Re: Converse of Schur's Theorem
Posted:
Apr 3, 2004 9:06 AM


Robin Chapman <rjc@ivorynospamtower.freeserve.co.uk> wrote in message news:<c4k8rp$br7$3@newsg2.svr.pol.co.uk>... >> 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?
Anvita



