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.
Citation
John S. Wilson. "First-order characterization of the radical of a finite group." J. Symbolic Logic 74 (4) 1429 - 1435, December 2009. https://doi.org/10.2178/jsl/1254748698
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