Results 1 to 10 of about 250 (108)
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
doaj +8 more sources
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
doaj +2 more sources
On Chernikov-by-nilpotent groups [PDF]
Let $γ_k=[x_1,\dots,x_k]$ be the $k$-th lower central group-word. Given a group $G$, we write $X_k(G)$ for the set of $γ_k$-values and $γ_k(G)$ for the $k$-th term of the lower central of $G$. This paper deals with groups in which $\langle g^{X_k(G)} \rangle$ is a Chernikov group of size at most $(m,n)$ for all $g\in G$. The main result is that $γ_{k+1}
Martina Capasso +2 more
+6 more sources
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.
Yuriy Drozd, Andriana I. Plakosh
openalex +4 more sources
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
doaj +2 more sources
Ayoub's theorem and Chernikov groups [PDF]
Journal of Group Theory, 2009 Let \(G=H\times K\) be the direct product of two groups \(H\) and \(K\) and suppose that \(G\) admits a normal subgroup \(N\) with \(N\simeq A\) and \(G/N\simeq B\). \textit{J. Ayoub} [in J. Group Theory 9, No. 3, 307-316 (2006; Zbl 1108.20030)] proved that if \(G\) is finite then \(N\) is a direct factor of \(G\).
B. A. F. Wehrfritz
openalex +3 more sources
Groups with all Subgroups Subnormal or Nilpotent-by-Chernikov
Rendiconti del Seminario Matematico della Università di Padova, 2011 An important result by \textit{W. Möhres} [Arch. Math. 54, No. 3, 232-235 (1990; Zbl 0663.20027)] shows that any group in which all subgroups are subnormal is soluble. Using this theorem, \textit{H. Smith} [Topics in infinite groups. Rome: Aracne. Quad. Mat.
Howard Smith
openalex +5 more sources
On nilpotent Chernikov 2-groups with elementary tops [PDF]
, 2016 We give an explicit description of nilpotent Chernikov 2-groups with elementary tops and the basis of rank 2.
Yuriy Drozd, Andriana I. Plakosh
openalex +4 more sources
On groups whose all proper subgroups have Chernikov derived subgroups [PDF]
Journal of Mathematical Sciences, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
N. N. Semko, O.A. Yarovaya
openalex +2 more sources
On certain groups with Chernikov group of automorphisms
Researches in Mathematics, 2014 We obtained automorphic analogue of Schur’s theorem for the case when an arbitrary subgroup A of automorphism group Aut(G) of a group G and the factor-group of a group G modulo A-center are Chernikov groups.
A.A. Pypka
openalex +3 more sources