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First-order characterization of the radical of a finite group

Published online by Cambridge University Press:  12 March 2014

John S. Wilson
John S. Wilson*
Affiliation:
University College, Oxford Ox1 4Bh, UK, E-mail: wilsonjs@maths.ox.ac.uk
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Abstract

It is shown that there is a formula σ(g) in the first-order language of group theory with the following property: for every finite group G, the largest soluble normal subgroup of G consists precisely of the elements g of G such that σ(g) holds.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 4 , December 2009 , pp. 1429 - 1435
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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