[seqfan] Re: Higman's group

Neil Sloane njasloane at gmail.com
Thu Feb 11 20:00:34 CET 2016


PS

Sorry, you were looking at the infinite Higman group, not the Higman-Sims
grp.
I don't know an easy way to compute that.

But what I said about the sporadic simple groups is still true - they are
worth
studying for their growth series

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 1:36 PM, Neil Sloane <njasloane at gmail.com> wrote:

> 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#>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>



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