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SUMMARY:Towards a nonsolvable Quotient Algorithm - Alexander Hulpke (Color
 ado State University)
DTSTART:20200130T101000Z
DTEND:20200130T110000Z
UID:TALK138178@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:[This is joint work with Heiko Dietrich from Monash U.]<br>Quo
 tient algorithms have been a principal tool for the computational<br>inves
 tigation of finitely presented groups as well as for constructing groups.<
 br>We describe a method for a nonsolvable quotient algorithm\, that extend
 s a<br>known finite quotient with a module.<br>Generalizing ideas of the $
 p$-quotient algorithm\, and building on results of<br>Gaschuetz on the rep
 resentation module\, we construct\, for a finite group<br>$H$\, an irreduc
 ible module $V$ in characteristic $p$\, and a given number of<br>generator
 s $e$ a covering group of $H$\, such that every $e$-generator<br>extension
  of $H$ with $V$ must be a quotient thereof. This construction uses<br>a m
 ix of cohomology (building on rewriting systems) and wreath product method
 s.<br>Evaluating relators of a finitely presented group in such a cover of
  a known<br>quotient then yields a maximal quotient associated to the cove
 r.<br>I will describe theory and implementation of such an approach and di
 scuss<br>the scope of the method.
LOCATION:Seminar Room 1\, Newton Institute
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