Quotient algorithms have been a principal tool for the computational

investigation of fi nitely presented groups as well as for constructin g groups.

We describe a method for a nonsolvabl e quotient algorithm\, that extends a

known fin ite quotient with a module.

Generalizing ideas of the $p$-quotient algorithm\, and building on re sults of

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

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

generators $e$ a covering gro up of $H$\, such that every $e$-generator

exten sion of $H$ with $V$ must be a quotient thereof. T his construction uses

a mix of cohomology (buil ding on rewriting systems) and wreath product meth ods.

Evaluating relators of a finitely presente d group in such a cover of a known

quotient the n yields a maximal quotient associated to the cove r.

I will describe theory and implementation of such an approach and discuss

the scope of the method. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR