subabquot:
Usage:     subabquot  [-c] gpname [inf1] [inf2] [outf]

gpname.inf1 contains permutation representation of finitely presented group
G=gpname. Default is gpname.ip.  If gpname.inf1 does not exist, then the
trivial permutation representation is used.

gpname.inf2 contains generators and relators of gpname in format output
by powrels. Default is inf2=powrels.

The abelian invariant factors of the subgroup of gpname that maps onto the
stabilizer of the point 1 in the permutation representation are output to
gpname.outf. Default is outf=subabquot.

If the -c flag is set, then if an integer bigger than 10000000 is encountered,
the program exits with error message. It is probably best to use this flag,
since integer overflow results in wrong answers.



foxreg:
Usage:    foxreg [-s] gpname [inf1] [inf2] [outf]

gpname.inf1 contains permutation representation of finitely presented group
G=gpname. Default is gpname.ip.  If gpname.inf1 does not exist, then the
trivial permutation representation is used.

gpname.inf2 contains generators and relators of gpname in format output
by powrels. Default is inf2=powrels.

Assuming that gpname.inf1 is a regular permutation group, let  K  be the
kernel of the epimorphism from the group gpname to this permutation group.
This program asks the user to input a prime  p, and then computes the
largest elementary abelian p-quotient K/L of  K.

If  -s  is set (can't remember why this is called -s!), then provided that
|G/L| has order less than about 2^16, the regular permutation representation
of  G/L  is output to  gpname.outf. (Default is outf=op.)



Typical usage to find soluble quotients of  group gpname.

Run subabquot gpname to get abelian quotients of group  G.
Find out for which primes  p  G  has nontrivial elementary abelian p-quotients.
For each such  p,  run  foxreg -s gpname. (Outputs permutation representation
to gpname.op, say).  Then  run
subabquot gpname op to get abelian quotients of kernel  K  of this
permutation representation. Find primes p for which  K  ahs nontrivial
elementary abelian p-quotients. Then run foxreg -s gpname op, etc.

When quotients  G/K  get big (bigger than a few hundred), integer overflow
may occur in subabquot. You can then always run  foxreg without -s,
and try different primes to see which occur in K/K'.

foxreg outputs a comment on the terminal giving dimension of  H^1(G,M).
This is the exponent of the largest elementary abelian p-quotient of K/K'.
