### A Propos E'Equations Generiques

Frank O. Wagner
Source: J. Symbolic Logic Volume 57, Issue 2 (1992), 548-554.

#### Abstract

We prove that a stable solvable group $G$ which satisfies $x^n = 1$ generically is of finite exponent dividing some power of $n$. Furthermore, $G$ is nilpotent-by-finite. A second result is that in a stable group of finite exponent, involutions either have big centralisers, or invert a subgroup of finite index (which hence has to be abelian).

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