Accessible Requires Authentication Published by De Gruyter September 13, 2006

On the probability of satisfying a word in a group

Miklós Abért
From the journal


We show that for any finite group G and for any d there exists a word wFd such that a d-tuple in G satisfies w if and only if it generates a solvable subgroup. As a corollary, the probability that a word is satisfied in a fixed non-solvable group can be made arbitrarily small; this answers a question of Alon Amit.

It also follows that there is no absolute bound in the Baumslag–Pride theorem for the minimal index in a group with at least two more generators than relators of a subgroup that can be mapped homomorphically onto a non-abelian free group.

(Communicated by J. S. Wilson)

Received: 2005-09-12
Published Online: 2006-09-13
Published in Print: 2006-09-01

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