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• W2054893295 abstract "Guralnick, Kunyavskii, Plotkin and Shalev have shown that the solvable radical of a finite group G can be characterized as the set of all x∈G such that 〈x,y〉 is solvable for all y∈G. We prove two generalizations of this result. Firstly, it is enough to check the solvability of 〈x,y〉 for every p-element y∈G for every odd prime p. Secondly, if x has odd order, then it is enough to check the solvability of 〈x,y〉 for every 2-element y∈G." @default.
• W2054893295 created "2016-06-24" @default.
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• W2054893295 date "2014-10-01" @default.
• W2054893295 modified "2023-09-27" @default.
• W2054893295 title "Criteria for solvable radical membership via p-elements" @default.
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• W2054893295 doi "https://doi.org/10.1016/j.jalgebra.2014.06.003" @default.
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