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12.48 (1992)

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Let $G$ be a sharply doubly transitive permutation group on a set $\Omega$ (see 11.52 for a definition).
$\qquad$ (a) Does $G$ possess a regular normal subgroup if a point stabilizer is locally finite?
$\qquad$ (b) Does $G$ possess a regular normal subgroup if a point stabilizer has an abelian subgroup of finite index?

Contributor: V. D. Mazurov

Progress

Comments of 2022: an affirmative answer to part (b) is obtained in permutation characteristic 0 (F. O. Wagner, Preprint, 2022, https://hal.archives-ouvertes.fr/hal-03590818).

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