# [seqfan] Re: Subquotients of sporadic simple groups

Neil Sloane njasloane at gmail.com
Wed Sep 30 20:10:35 CEST 2015

```So after the removal of A262401, is it true that
we don't yet have the Subquotients of sporadic simple groups
sequence? Charles, did you ask Rob Wilson? He will
surely know the answer. Or do you want me to ask him?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Email: njasloane at gmail.com

On Thu, Sep 24, 2015 at 7:08 PM, Sven Simon <sven-h.simon at gmx.de> wrote:

> Hello,
>
> the Pari program I wrote for the sequence (sequence number 262401) says
> a[26] = 24. So there was a difference to the value Charles had written in
> his email. I looked a bit deeper in the topic and found that with
> subquotient was meant something more than pure division, coming from group
> theory. So sequence 262401 is completly nonsense and I would like to remove
> it.
> Sorry for that.
>
> Sven
>
> -----Ursprüngliche Nachricht-----
> Von: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] Im Auftrag von Charles
> Greathouse
> Gesendet: Donnerstag, 17. September 2015 20:24
> An: Sequence Fanatics Discussion list
> Betreff: [seqfan] Subquotients of sporadic simple groups
>
> Arrange the sporadic simple groups by increasing order 1, 2, ..., 26, then
> define a(n) = Number of sporadic simple groups which are subquotients of
> the n-th largest sporadic simple group.
>
> I don't think this sequence is in the OEIS, and it seems interesting. Are
> all these terms known? Can this sequence be added to the OEIS?
>
> It's well-known that a(26) = 20, the so-called "happy family". Trivially
> a(1) = 1 and a(2) = 2 since M11 is a subquotient of M12 (and itself). a(3)
> = 1 since the Janko group J1 has order 2^3 * ... and 2^4 divides the orders
> of M11 and M12.
>
> I've seen diagrams giving (the transitive reduction of) the subquotient
> relationships, but I don't know if they're known to be complete. If not,
> what's the smallest group with an open question?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
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