Results 1 to 10 of about 2,730 (156)
On nilpotent Chernikov p-groups with elementary tops [PDF]
Archiv der Mathematik, 2014 The description of nilpotent Chernikov $p$-groups with elementary tops is reduced to the study of tuples of skew-symmetric bilinear forms over the residue field $\mathbb{F}_p$. If $p\ne2$ and the bottom of the group only consists of $2$ quasi-cyclic summands, a complete classification is given. We use the technique of quivers with relations.
Drozd, Yuriy, Plakosh, Andriana
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Locally finite groups containing a $2$-element with Chernikov centralizer [PDF]
Monatshefte für Mathematik, 2014 Suppose that a locally finite group $G$ has a $2$-element $g$ with Chernikov centralizer. It is proved that if the involution in $\langle g\rangle$ has nilpotent centralizer, then $G$ has a soluble subgroup of finite index.
Evgeny Khukhro +2 more
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Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov
Open Mathematics, 2012 Abstract Let G be a locally finite group satisfying the condition given in the title and suppose that G is not nilpotent-by-Chernikov. It is shown that G has a section S that is not nilpotent-by-Chernikov, where S is either a p-group or a semi-direct product of the additive group A of a locally finite field F by a subgroup K of the ...
Cutolo Giovanni, Smith Howard
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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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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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Weak Engel Conditions on Linear Groups [PDF]
Advances in Group Theory and Applications, 2019 We study several weak Engel conditions on linear groups, starting from the “almost Engel” condition of Khukhro and Shumyatsky. There the groups were Engel modulo certain finite subsets.
B.A.F. Wehrfritz
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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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Қарағанды университетінің хабаршысы. Математика сериясы, 2020 We consider the problem of recognizing a group by its bottom layer. This problem is solved in the class of layer-finite groups. A group is layer-finite if it has a finite number of elements of every order. This concept was first introduced by S.
V.I. Senashov, I.A. Paraschuk
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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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Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov [PDF]
International Journal of Group Theory, 2012 We pursue further our investigation, begun in [H.~Smith, Groups with all subgroups subnormal or nilpotent-by-{C}hernikov, emph{Rend. Sem. Mat. Univ. Padova} 126 (2011), 245--253] and continued in [G.~Cutolo and H.~Smith, Locally finite groups with all ...
H. Smith, G. Cutolo
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