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On the probability of satisfying a word in a group | Miklos Abert
; | Date: |
15 Apr 2005 | Subject: | Group Theory | math.GR | Abstract: | We show that for any finite group $G$ and for any $d$ there exists a word $win F_{d}$ such that a $d$-tuple in $G$ satisfies $w$ if and only if it generates a solvable subgroup. In particular, if $G$ itself is not solvable, then it cannot be obtained as a quotient of the one relator group $F_{d}/$. As a corollary, the probability that a word is satisfied in a fixed non-solvable group can be made arbitrarily small, answering a question of Alon Amit. | Source: | arXiv, math.GR/0504312 | Services: | Forum | Review | PDF | Favorites |
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