[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
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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