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11.96 (1990)

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(a) Is it true that, for a given number $n$, there exist only finitely many finite simple groups each of which contains an involution which commutes with at most $n$ involutions of the group?
(b) Is it true that there are no infinite simple groups satisfying this condition?

Contributor: S. P. Strunkov

Progress

Editors’ comments: (a) Yes, it is true (mod CFSG); moreover, if a locally finite group has such an involution, then it is finite of $n$-bounded order (S. V. Skresanov, J. Group Theory, 27, no. 6 (2024), 1197–1202).

(b) No, since $PSL_2(\mathbb{R})$ is an infinite simple group, which contains an involution but does not contain a subgroup isomorphic to the Klein 4-group (S. V. Skresanov, J. Group Theory, 27, no. 6 (2024), 1197–1202).

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