Journal of Symbolic Logic

First-order characterization of the radical of a finite group

John S. Wilson

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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.

Article information

Source
J. Symbolic Logic, Volume 74, Issue 4 (2009), 1429-1435.

Dates
First available in Project Euclid: 5 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1254748698

Digital Object Identifier
doi:10.2178/jsl/1254748698

Mathematical Reviews number (MathSciNet)
MR2583827

Zentralblatt MATH identifier
1184.03030

Citation

Wilson, John S. First-order characterization of the radical of a finite group. J. Symbolic Logic 74 (2009), no. 4, 1429--1435. doi:10.2178/jsl/1254748698. https://projecteuclid.org/euclid.jsl/1254748698


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