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6.57 (1978)

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A group $G$ is said to be (conjugacy, $p$-conjugacy) biprimitively finite if, for any finite subgroup $H$, any two elements of prime order (any two conjugate elements of prime order, of prime order $p$) in $N_G(H)/H$ generate a finite subgroup. Do the elements of finite order in a (conjugacy) biprimitively finite group $G$ form a subgroup (the periodic part of $G$)?

Contributor: V. P. Shunkov

Progress

Not always (A. A. Cherep, Algebra and Logic, 29 (1987), 311–313).

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