ON THE HYPERDECIDABILITY OF PSEUDOVARIETIES OF GROUPS

Abstract

Clarifying the relation between Ash's (algebraic-combinatorial) proof and Ribes and Zalesski[Formula: see text]'s (topological) proof of the Rhodes Type II conjecture is an intriguing and interesting question which arose when both proofs appeared in the beginning of the 1990s. Attempting to contribute to this clarification, we observe that two sets, each playing a crucial role in one of the proofs, are in fact equal. The equality of these sets allows us to give an alternative proof of part of the main theorem of Ash's paper where the hyperdecidability of the pseudovariety of all finite groups is established.