Quotient algorithms have been a principa l tool for the computational

investigation of finitely presented groups as well as for construct ing groups.

We describe a method for a nonsolv able quotient algorithm\, that extends a

known finite quotient with a module.

Generalizing i deas of the $p$-quotient algorithm\, and building on results of

Gaschuetz on the representation module\, we construct\, for a finite group

$H$ \, an irreducible module $V$ in characteristic $p$ \, and a given number of

generators $e$ a cove ring group of $H$\, such that every $e$-generator< br> extension of $H$ with $V$ must be a quotient t hereof. This construction uses

a mix of cohomo logy (building on rewriting systems) and wreath pr oduct methods.

Evaluating relators of a finite ly presented group in such a cover of a known

quotient then yields a maximal quotient associated to the cover.

I will describe theory and impl ementation of such an approach and discuss

the scope of the method. LOCATION:Seminar Room 1\, Newton Institute CONTACT:info@newton.ac.uk END:VEVENT END:VCALENDAR