[seqfan] Re: Higman's group

Neil Sloane njasloane at gmail.com
Thu Feb 11 19:36:58 CET 2016


I'm very interested!  The trouble is, these series have several different
names, which makes it hard to search the OEIS for them. "Growth series"
is one name that is commonly used. Also sometimes "Poincare series",
even "Hilbert series", also "Length function". (But Poincare series etc
more often refers to
the number of indep. invariants of each degree, so one has to be careful.)

It would be nice if we had the growth series for all the sporadic simple
groups, not just Higman-Sims.
It would be a worthwhile project to do this systematically.

I think MAGMA can do this, and MAGMA certainly contains all the groups.

Another difficulty is that the growth series depends on the choice of
generators.
So these growth series are in general not well-defined, even for the
classical groups.

What I suggest is, work out some examples for smaller sporadic groups,
look them up in the OEIS, find the MAGMA programs. Let me know what you
find!





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.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Thu, Feb 11, 2016 at 12:02 PM, David Newman <davidsnewman at gmail.com>
wrote:

> I'm trying to calculate the number of elements of length n in Higman's
> group (See *https://en <https://en>.wikipedia.org/wiki/Higman_group    for
> example.)*
> The numbers that I get so far are 1 , 8 , 56 , 352, which wasn't in the
> OEIS
> when I looked.
>
> Anyone interested?
> <https://www.google.com/?gws_rd=ssl#>
>
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> Seqfan Mailing list - http://list.seqfan.eu/
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