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This article is cited in 2 scientific papers (total in 2 papers)
On groups with involutions saturated by finite Frobenius groups
B. E. Durakov, A. I. Sozutov Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk
Abstract:
We study the mixed and periodic groups with involutions and finite elements which are saturated by finite Frobenius groups. We prove that a group $G$ of $2$-rank $1$ of even order greater than $2$ splits into the direct product of a periodic abelian group $F$ and the centralizer of an involution; moreover, each maximal periodic subgroup in $G$ is a Frobenius group with kernel $F$. We characterize one class with the saturation condition. We prove that a group of $2$-rank greater than $1$ with finite elements of prime orders is a split extension of a periodic group $F$ by a group $H$ in which all elements of prime orders generate a locally cyclic group; moreover, every element in $F$ with every element of prime order in $H$ generates a finite Frobenius group. Under the condition of the triviality of the local finite radical, we determine some properties of the subgroup $F$.
Keywords:
Frobenius group, involution, $2$-rank, finite element, weakly conjugate biprimitive finite group, saturation.
Received: 17.03.2022 Revised: 21.04.2022 Accepted: 15.06.2022
Citation:
B. E. Durakov, A. I. Sozutov, “On groups with involutions saturated by finite Frobenius groups”, Sibirsk. Mat. Zh., 63:6 (2022), 1256–1265; Siberian Math. J., 63:6 (2022), 1075–1082
Linking options:
https://www.mathnet.ru/eng/smj7729 https://www.mathnet.ru/eng/smj/v63/i6/p1256
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