Affiliation:
1. UFR de Mathématiques, Bâtiment Sophie Germain , Université de Paris , 8 place Aurélie Nemours, 75013 Paris , France
Abstract
Abstract
We systematically study groups whose marked finite quotients form a recursive set.
We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth function and solvability of the word problem.
We give examples of infinitely presented groups whose finite quotients can be effectively enumerated.
Finally, our main result is that a residually finite group can fail to be recursively presented and still have computable finite quotients, and that, on the other hand, it can have solvable word problem but not have computable finite quotients.
Subject
Algebra and Number Theory
Cited by
1 articles.
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