[seqfan] Re: Is A037289 multiplicative

israel at math.ubc.ca israel at math.ubc.ca
Tue Jul 10 18:09:07 CEST 2012


It should be stated, I think, that these are not necessarily rings with 
identity.

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
>
>
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