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Topic: Converse of Schur's Theorem
Replies: 2   Last Post: Apr 3, 2004 9:06 AM

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Posts: 29
Registered: 12/13/04
Re: Converse of Schur's Theorem
Posted: Apr 3, 2004 9:06 AM
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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?


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