Computability of finite quotients of finitely generated groups

Emmanuel Rauzy

Published 2020-02-06Version 1

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups. We emphasize the link with the depth function of residually finite groups. Finally, we show that a residually finite group can be even not recursively presented and still have computable finite quotients, and that, on the other hand, it can have solvable word problem while still not having computable finite quotients.