# [seqfan] Re: Subquotients of sporadic simple groups

Sven Simon sven-h.simon at gmx.de
Fri Sep 25 01:08:00 CEST 2015

```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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