On the difficulty of recognising finite quotients of finitely presented groups (Martin Bridson, Oxford)

14.05.2019 14:15

Following my earlier work with Wilton, one knows that that there is no alogrithm that, given a finitely presented group, can decide whether or not the given group has a non-trivial finite quotient. This implies that there is no algorithm that can recognise the existence of quotients that lie in at least one of the classical families of finite simple groups -- but for which families is there an algorithm and for which families is there no algorithm? In joint work with Evans, Liebeck and Segal, I answer this question. It turns out, for example, that if one fixes d and lets q vary, then one can decide whether a finitely presented group has a quotient of the form SL(d,q), but if one fixes q and lets d vary, then one cannot decide.

Lieu

Room 624, Att. unusual time and place, Séminaire "Groupes et Géométrie"

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