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Criteria for solvable radical membership via p-elements
Guralnick, Kunyavskii, Plotkin and Shalev have shown that the solvable
radical of a finite group can be characterized as the set of all
such that is solvable for all $y\in G$. We prove two generalizations of
this result. Firstly, it is enough to check the solvability of for
every -element for every odd prime . Secondly, if has odd
order, then it is enough to check the solvability of for every
2-element .Comment: 17 page
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