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6.62 (1978)

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Is a (conjugacy, $p$-conjugacy) biprimitively finite group (see 6.57) finite if it has a finite maximal subgroup ($p$-subgroup)?

Contributor: V. P. Shunkov

Progress

There are affirmative answers for conjugacy biprimitively finite $p$-groups and for 2-conjugacy biprimitively finite groups (V. P. Shunkov, Algebra and Logic, 9, no. 4 (1970), 291–297; 11, no. 4 (1972), 260–272; 12, no. 5 (1973), 347–353), while the statement does not hold for arbitrary periodic groups, see also 3.9.

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