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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 =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

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