Results 1 to 10 of about 77 (67)

On Two Properties of Shunkov Group

Известия Иркутского государственного университета: Серия "Математика", 2021
One of the interesting classes of mixed groups ( i.e. groups that can contain both elements of finite order and elements of infinite order) is the class of Shunkov groups. The group $G$ is called Shunkov group if for any finite subgroup $H$ of $G$ in the
A.A. Shlepkin, I. V. Sabodakh
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On Shunkov Groups Saturated with Finite Groups

Известия Иркутского государственного университета: Серия "Математика", 2018
The structure of the group consisting of elements of finite order depends to a large extent on the structure of the finite subgroups of the group under consideration. One of the effective conditions for investigating an infinite group containing elements
A.A. Shlepkin
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On the Shunkov groups acting freely on Abelian groups

Siberian Mathematical Journal, 2013
A group \(G\) is called a \textit{Shunkov group} if, for each finite subgroup \(F\) of \(G\), the subgroup generated by any two conjugate elements of prime order in the group \(N_G(F)/F\) is finite. With Theorem 1 the author proves that the set of elements of finite order in a Shunkov group of rank \(1\) (i.e. \(C_p\times C_p\)-free for all primes \(p\)
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On Periodic Shunkov’s Groups with Almost Layer-finite Normalizers of Finite Subgroups

Известия Иркутского государственного университета: Серия "Математика", 2021
Layer-finite groups first appeared in the work by S.~N.~Chernikov (1945). Almost layer-finite groups are extensions of layer-finite groups by finite groups.
V.I. Senashov
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On Periodic Groups of Shunkov with the Chernikov Centralizers of Involutions

Известия Иркутского государственного университета: Серия "Математика", 2020
Layer-finite groups first appeared in the work by S.~N.~Chernikov (1945). Almost layer-finite groups are extensions of layer-finite groups by finite groups.
V.I. Senashov
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Locally Finite Groups Saturated with Direct Product of Two Finite Dihedral Groups

Известия Иркутского государственного университета: Серия "Математика", 2023
In the study of infinite groups, as a rule, some finiteness conditions are imposed. For example, the group is required to be periodic, Shunkov group, Frobenius group, locally finite group.
A. V. Kukharev, A.A. Shlepkin
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New classes of infinite groups [PDF]

Iranian Journal of Numerical Analysis and Optimization, 2008
In this article, we consider some new classes of groups, namely, Mp-groups, T0-groups,Ø-groups,Ø0-groups, groups with finitely embedded involution, which were appeared at the end of twenties century.
V.I. Senashov, V.P. Shunkov
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Properties of groups with points [PDF]

Iranian Journal of Numerical Analysis and Optimization, 2009
In this paper, we consider groups with points which were introduced by V.P. Shunkov in 1990. In Novikov-Adian's group, Adian's periodic products of finite groups without involutions and Olshansky's periodic monsters every non-unit element is a point ...
V.I. Senashov, E.N. Takovleva
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Groups with a Strongly Embedded Subgroup Saturated with Finite Simple Non-abelian Groups

Известия Иркутского государственного университета: Серия "Математика", 2020
An important concept in the theory of finite groups is the concept of a strongly embedded subgroup. The fundamental result on the structure of finite groups with a strongly embedded subgroup belongs to M. Suzuki.
A.A. Shlepkin
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On a Sufficient Condition for the Existence of a Periodic Part in the Shunkov Group

Известия Иркутского государственного университета: Серия "Математика", 2017
The group $ G $ is saturated with groups from the set of groups if any a finite subgroup $ K $ of $ G $ is contained in a subgroup of $ G $, which is isomorphic to some group in $ \mathfrak{X} $.
A.A. Shlepkin
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