I love the extensions to GAP which allow it to perform operations on finitely
generated groups (since I'm a topologist by profession), but have run into
a problem of sorts. I have two presentations of the same group (I know that
they are isomorphic for other reasons) that I would like to work with in GAP.
The problem is, while GAP can compute the order of the group quite easily
for one of the presentations, for the other it has EXTREME difficulty. The
group is of order 120 and I usually run GAP with 2MB of allocated storage.
However, GAP crashes on the second presentation with this memory size. The
only way I've been able to get it to compute the order was to run GAP without
the memory size restriction on a machine which has 128MB of resident memory.
CAYLEY has no problem with either presentation UNLESS one uses the Felsch
algorithm on the second presentation. It then goes into an infinite loop
and crashes pretty hard.
I'm not sure if this is a bug (since my standalone Todd-Coxeter will compute
either of these in under 10 seconds) or a limitation of the particular
implementation of Todd-Coxeter that's resident in GAP.
Here are the output files from the two runs. The first is for the presentation
which GAP has no problems with. The second is the presentation which causes
all the difficulty.
(Note: I am running GAP on a 20 processor Sequent with 128MB of memory using
the DYNIX/ptx operating system (a System V variant)).
------------Output File #1-------------------------------------------------
######## Lehrstuhl D fuer Mathematik
### #### RWTH Aachen
## ##
## # ####### #########
## # ## ## # ##
## # # ## # ##
#### ## ## # # ##
##### ### ## ## ## ##
######### # ######### #######
# #
## Version 3 #
### Release 1 #
## # 7 Apr 92 #
## #
## # Johannes Meier, Martin Schoenert
## # Alice Niemeyer, Werner Nickel
## # Alex Wegner, Thomas Bischops
### ## Juergen Mnich, Frank Celler
###### Thomas Breuer, Goetz Pfeiffer
Udo Polis
For help enter: ?<return>
gap> g := FreeGroup( 2, "g" );
Group( g.1, g.2 )
gap> g.relators := [ g.1^5*g.2^-8, g.2*g.1*g.2^-1*g.1^-4 ];
[ g.1^5*g.2^-8, g.2*g.1*g.2^-1*g.1^-4 ]
gap> Size( g );
120
gap> time;
1240
gap> quit;
----------------End of Output File-----------------------------------------
----------------Output File #2---------------------------------------------
######## Lehrstuhl D fuer Mathematik
### #### RWTH Aachen
## ##
## # ####### #########
## # ## ## # ##
## # # ## # ##
#### ## ## # # ##
##### ### ## ## ## ##
######### # ######### #######
# #
## Version 3 #
### Release 1 #
## # 7 Apr 92 #
## #
## # Johannes Meier, Martin Schoenert
## # Alice Niemeyer, Werner Nickel
## # Alex Wegner, Thomas Bischops
### ## Juergen Mnich, Frank Celler
###### Thomas Breuer, Goetz Pfeiffer
Udo Polis
For help enter: ?<return>
gap> g := FreeGroup( 2, "g" );
Group( g.1, g.2 )
gap> g.relators := [ g.1^5*g.2^-24, g.2*g.1^2*g.2^-1*g.1^-3 ];
[ g.1^5*g.2^-24, g.2*g.1^2*g.2^-1*g.1^-3 ]
gap> Size( g );
120
gap> time;
2238310
gap> quit;
------------------End of Output File-------------------------------------
--John Neil
John Neil, Graduate Teaching Assistant e-mail: neil@math.mth.pdx.edu Mathematics Department NeXTMail: neil@dehn.mth.pdx.edu Portland State University =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=