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- W3137142010 abstract "A group is called weakly conjugate biprimitively finite if each its element of prime order generates a finite subgroup with any of its conjugate elements. A binary finite group is a periodic group in which any two elements generate a finite subgroup. If $mathfrak{X}$ is some set of finite groups, then the group $G$ saturated with groups from the set $mathfrak{X}$ if any finite subgroup of $G$ is contained in a subgroup of $G$, isomorphic to some group from $mathfrak{X}$. A group $G = F leftthreetimes H$ is a Frobenius group with kernel $F$ and a complement $H$ if $H cap H^f = 1$ for all $f in F^{#}$ and each element from $G setminus F$ belongs to a one conjugated to $H$ subgroup of $G$. In the paper we prove that a saturated with finite Frobenius groups periodic weakly conjugate biprimitive finite group with a nontrivial locally finite radical is a Frobenius group. A number of properties of such groups and their quotient groups by a locally finite radical are found. A similar result was obtained for binary finite groups with the indicated conditions. Examples of periodic non locally finite groups with the properties above are given, and a number of questions on combinatorial group theory are raised." @default.
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- W3137142010 date "2021-01-01" @default.
- W3137142010 modified "2023-09-26" @default.
- W3137142010 title "On Periodic Groups Saturated with Finite Frobenius Groups" @default.
- W3137142010 doi "https://doi.org/10.26516/1997-7670.2021.35.73" @default.
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