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12.27 (1992)

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Let $G$ be a simple locally finite group. We say that $G$ is a group of finite type if there is a non-trivial permutational representation of $G$ such that some finite subgroup of $G$ has no regular orbits. Investigate and, perhaps, classify the simple locally finite groups of finite type. Partial results see in (B. Hartley, A. Zalesski, Isr. J. Math., 82 (1993), 299–327, J. London Math. Soc., 55 (1997), 210–230; F. Leinen, O. Puglisi, Illinois J. Math., 47 (2003), 345–360).

Contributor: A. E. Zalesskiĭ

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