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COMPONENTS AND MINIMAL NORMAL SUBGROUPS OF FINITE AND PSEUDOFINITE GROUPS
Published online by Cambridge University Press: 14 March 2019
Abstract
It is proved that there is a formula $\pi \left( {h,x} \right)$ in the first-order language of group theory such that each component and each non-abelian minimal normal subgroup of a finite group G is definable by $\pi \left( {h,x} \right)$ for a suitable element h of G; in other words, each such subgroup has the form $\left\{ {x|x\pi \left( {h,x} \right)} \right\}$ for some h. A number of consequences for infinite models of the theory of finite groups are described.
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- Copyright © The Association for Symbolic Logic 2019