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17.55 (2010)

Solved

Does there exist an absolute constant $k$ such that for any prefrattini subgroup $H$ in any finite soluble group $G$ there exist $k$ conjugates of $H$ whose intersection is $\Phi(G)$?

Contributor: S. F. Kamornikov

Progress

Yes, such a constant exists and is equal to 3 (S. F. Kamornikov, Int. J. Group Theory, 6, no. 2 (2017), 1–5).

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