> < ^ From:

< ^ Subject:

Dear Laurent,

> hello again,

> i ran in a few new other problems with gap, which are:

>

> i cannot define a group algebra over an infinite non-free group:

> gap> G := FreeGroup("a","b");

> <free group on the generators [ a, b ]>

> gap> GroupRing(GF(2),G);

> <algebra-with-one over GF(2), with 4 generators>

> gap> G := G / [Comm(G.1,G.2)];

> <fp group on the generators [ a, b ]>

> gap> GroupRing(GF(2),G);

> Error the coset enumeration has defined more than 256000 cosets:

The situation here is a bit complicated: The way group rings are represented,

it is assumed that the group elements can be sorted with respect to <. For

finitely presented groups, defining a computable total order however is

quite hard -- what GAP 4.2 does is to order via a faithful permutation

representation. This obviously fails here.

In the development version, there is code which will try the coset

enumeration only to a certain limit and then use a (as mentioned before: much

better performing that in 4.2...) Knuth-Bendix and compare word normal forms.

With this, your example seems to work:

gap> r:=GroupRing(GF(2),G); <algebra-with-one over GF(2), with 4 generators> gap> r.1*r.2+r.3*r.4; (Z(2)^0)*a^-1*b^-1+(Z(2)^0)*a*b gap> last^5; (Z(2)^0)*a^-1*b^-1*a^-1*b^-1*a^-1*b^-1*a^-1*b^-1*a*b+(Z(2)^ 0)*a*b*a*b*a*b*a*b*a^-1*b^-1+(Z(2)^0)*a^-1*b^-1*a^-1*b^-1*a^-1*b^-1*a^-1*b^ -1*a^-1*b^-1+(Z(2)^0)*a*b*a*b*a*b*a*b*a*b

Alas, this is only in the development version and not in 4.2 and will not be

part of a bug fix. (I can only repeat my offer in my last forum mail, if you

are willing to play around with slightly undocumented beta code.)

> concerning coset enumeration, couldn't it be possible to set up a flag in

> a group structure that the group is infinite, so that gap does not attempt

> element or coset enumeration, but rather answers by an error message?

Indeed. I have added code in the development version now that will avoid a

coset enumeration in this case. Thanks!

All the best,

Alexander

> < [top]