From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Newsgroups: sci.math.research
Subject: Re: Monster group
Date: 24 Sep 1996 17:31:50 GMT

In article <528fmc$bl@rzsun02.rrz.uni-hamburg.de>,
Hauke Reddmann <fc3a501@AMRISC01.math.uni-hamburg.de> wrote:
>Can anyone give me the prime factorization of n,
>n+1 and n-1, where n is the number of elements of
>the biggest simple (Monster) group?

Actually it's the largest among the 26 _sporadic_ _finite_ simple groups; the
other finite simple groups (the alternating groups and the groups of
Lie type) include groups of arbitrarily large order. I think it's
fair to say we have no real idea what the collection of _all_ simple
groups looks like.

The Monster has order  n=
     808017424794512875886459904961710757005754368000000000
     2^46 3^20 5^9 7^6 11^2 13^3 17 19 23 29 31 41 47 59 71
The prime factorization of  n  was of key importance in the generation
of "monstrous moonshine", a series of investigations by Conway et al
relating this group to automorphic forms.

I have no clue on the other hand why you would want the factorization
of n +- 1 but:

  n+1 = (18250906752127213)*(44272727693397225537389001926419074277)
  n-1 = (1471)*(6149167)*(5747201032159)*(15543018973958611922865137163473)
                       
These factorizations obtained with Montgomery's Elliptic Curve program.

dave