[seqfan] Re: Is A037289 multiplicative

israel at math.ubc.ca israel at math.ubc.ca
Tue Jul 10 09:35:08 CEST 2012

Doesn't the Sylow p-subgroup consist of all elements x such that p^m x = 0, 
where p^m is the largest power of p in n? Those elements constitute an 
ideal of R, since p^m (xy) = (p^m x) y = 0, and therefore in particular a 

Robert Israel
University of British Columbia

On Jul 9 2012, franktaw at netscape.net wrote:

>Looking at this sequence, there is a conjecture that the sequence is 
>multiplicative. I can almost prove that it is.
>I need a lemma that, if R is a commutative ring of order n, and prime p 
>divides n, then there is a Sylow p-subgroup of the additive group of R 
>that is in fact a subring if R. It is then easy to see that R must be 
>the direct product of these subrings, and the result follows.
>(This is an equivalent assertion, by the way; if there is a commutative 
>ring with no such "Sylow p-subring", the sequence is not multiplicative 
>for that n.)
>Does anybody know of such a result? Or can you find a proof?
>Franklin T. Adams-Watters
>Seqfan Mailing list - http://list.seqfan.eu/

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