[seqfan] Re: Symmetric group S_n as product of at most A225788(n) cyclic subgroups.
Charles Greathouse
charles.greathouse at case.edu
Thu May 23 22:58:46 CEST 2013
I think the sequence can be defined unambiguously: Smallest k such that the
symmetric group S_n is a product of at most k cyclic subgroups. I would
love to see this sequence in the OEIS. Do we have any GAP experts who can
code this up?
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
On Thu, May 23, 2013 at 3:56 PM, L. Edson Jeffery <lejeffery2 at gmail.com>wrote:
> According to Miklós Abért (see A225788), the symmetric group S_n is a
> product of at most 72*n^(1/2)*(log(n))^(3/2) cyclic subgroups. I took the
> floor() of this expression and recently submitted the sequence as A225788.
> Neil Sloane asked if the sequence of true values is in OEIS, that is, the
> sequence with definition "S_n is the product of (exactly) a(n) cyclic
> subgroups."
>
> I tried to work on this but failed. It is not even clear to me that the
> sequence can be determined unambiguously because if S_n = G_1 X G_2 X ... X
> G_k, for some k > 1, then it seems possible that also S_n = H_1 x ... x
> H_j, for some j != k, where the G's and H's are cyclic subgroups, and
> (where it should be that) j and k depend on the factorization of n. If not
> in OEIS and someone would like to figure this out and submit it, that would
> be greatly appreciated. Otherwise, if someone finds the sequence in the
> database, then either way please let me know the A-number so I can point
> A225788 to it. Thanks.
>
> Ed Jeffery
>
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