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7.16 (1980)

Solved

If $H$ is a proper subgroup of a finite group $G$, is there always an element of prime-power order not conjugate to an element of $H$?

Contributor: R. L. Griess

Progress

Yes, always (mod CFSG) (B. Fein, W. M. Kantor, M. Schacher, J. Reine Angew. Math., 328 (1981), 39–57).

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