Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Anvita

Posts: 29
Registered: 12/13/04
Re: Converse of Schur's Theorem
Posted: Apr 3, 2004 9:06 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


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




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.