> < ^ Date: Mon, 24 Nov 2003 09:16:50 -0700 (MST)
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
< ^ Subject: Re: The order of a finitely presented group.

Dear Gap-Forum,

Peter Campbell wrote:

While running a program the following "silly" presentation was discovered:
< a,b | a^2*b*a^-1, b*a^2*b^-1, a^-3 >.

GAP calculates the order of the group defined by this presentation to be 3

(I had replied already a couple of days ago directly to the poster, but now
got alerted that the mail had gon to the forum and not only to our
support/bug report address gap-trouble@dcs.st-and.ac.uk.)

Thank you for reporting this bug. When calculating the size of a finitely
presented group, GAP first enumerates the cosets of a cyclic subgroup and
then rewrites the presentation to this subgroup. (In this case rewriting is
almost trivial.) Alas this ``cyclic'' rewriting code in GAP4.3 has a bug
that can cause a too-large exponent to be created. This bug will be
corrected in the next bugfix/release.

Calculating the size of a finitely presented group is the *only* place where
this bug will arise, the general rewriting routines (even if the subgroup
happens to be cyclic) are not affected.

If you need workaround code please send us mail at

Apologies for this problem,

Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288

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