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10.77 (1986)

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Suppose that $G$ is a periodic group containing an elementary abelian subgroup $R$ of order 4. Must $G$ be locally finite
$\qquad$ a) if $C_G(R)$ is finite?
$\qquad$ b) if the centralizer of every involution of $R$ in $G$ is a Chernikov group?

Contributor: V. P. Shunkov

Progress

Remark of 1999: P. V. Shumyatsky (Quart. J. Math. Oxford (2), 49, no. 196 (1998), 491–499) gave a positive answer to the question a) in the case where $G$ is residually finite.

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