GAG 2019

Recognising finite quotients of finitely presented groups

 

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Wilton and I proved that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient. After recalling some elements of the proof of this theorem, I shall describe subsequent work with Evans, Liebeck and Segal that explores how decidability varies as one replaces the family of all finite quotients with families of finite simple quotients.