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COMPONENTS AND MINIMAL NORMAL SUBGROUPS OF FINITE AND PSEUDOFINITE GROUPS

Published online by Cambridge University Press:  14 March 2019

JOHN S. WILSON
JOHN S. WILSON*
Affiliation:
CHRIST’S COLLEGE CAMBRIDGE CB2 3BU, UKE-mail: jsw13@cam.ac.uk
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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.

Keywords

03C6003C1320E15group componentsfirst-orderpseudofinite groups

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 1 , March 2019 , pp. 290 - 300
Copyright
Copyright © The Association for Symbolic Logic 2019 

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