Results 131 to 140 of about 9,034,965 (157)

Matrix representation of groups of exterior automorphisms of Chernikov groups

Algebra and Logic, 1969
Yu I Merzlyakov
exaly   +2 more sources

Locally Nilpotent p-Groups Whose Proper Subgroups Are Hypercentral-by-Chernikov

, 2018
If is a group theoretical property or class of groups then a group G is a -group if G has the property or is a member of the class Let G be a group andbe a property of groups. If every proper subgroup of G satisfies but G itsellf doesnot satisfy it, then G is called a minimal non- group (We denote the classes ofminimal non- group by -group).
Arıkan, Aynur
core   +3 more sources

On Groups with Chernikov Centralizer of a 2-Subgroup

1996
Pavel Shumyatsky
exaly   +2 more sources

Groups With Chernikov Classes of Conjugate Subgroups

Journal of Group Theory, 2005
A famous theorem by B.~H.~Neumann states that a group \(G\) is central-by-finite if and only if each subgroup of \(G\) has finitely many conjugates, i.e. if and only if the index \(|G:N_G(H)|\) is finite for every subgroup \(H\) of \(G\). A group \(G\) is said to have `Chernikov conjugacy classes' of subgroups if \(G/N_G(H)_G\) is a Chernikov group for
Kurdachenko, Leonid A., Otal, Javier
openaire   +1 more source

Chernikov 2-Groups with Kleinian Top and Totally Reducible Bottom

Ukrainian Mathematical Journal, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Drozd, Yu. A., Plakosh, A. I.
openaire   +2 more sources

Groups with Bounded Chernikov Conjugate Classes of Elements

Ukrainian Mathematical Journal, 2002
A group \(G\) is called a group with Chernikov conjugacy classes (or CC-group) if \(G/C_G(g^G)\) is a Chernikov group for all \(g\in G\). The authors study such groups under the following restrictions on the quotient groups \(G/C_G(g^G)\) (BCC-groups): there exist two positive integers \(M(G)\) and \(O(G)\) such that \([G:C_G(g^G)]\leq O(G)\) for all \(
Kurdachenko, L.A., Otal, J., Subbotin, I.Ya.   +2 more
openaire   +3 more sources

Ayoub's theorem and Chernikov groups

Journal of Group Theory, 2010
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 \(G\).
openaire   +2 more sources

On locally finite groups with a Chernikov maximal subgroup

Algebra and Logic, 1998
The following theorem is proven: Let \(G\) be a locally finite group with Chernikov maximal subgroup \(H\) and let \(H\) contain no nontrivial normal subgroups of \(G\); then either \(G\) is finite or there exists an infinite normal elementary Abelian subgroup \(V\) of \(G\) such that \(G=VH\) and \(V\cap H=1\).
openaire   +2 more sources

Quotient groups of locally graded groups and groups of certain Kurosh-Chernikov classes

Ukrainian Mathematical Journal, 1998
The paper deals with the class of locally graded groups such that each non-unit finitely generated subgroup of the group contains a non-unit subgroup of finite index; the class of RN-groups consists of groups with solvable subinvariant subgroup system; the class of RI-groups consists of groups with solvable invariant system.
Chernikov, N. S., Trebenko, D. Ya.
openaire   +2 more sources

Groups in which every proper subgroup is ?ernikov-by-nilpotent or nilpotent-by-?ernikov

Archiv der Mathematik, 1988
\textit{B. Bruno} and \textit{R. E. Phillips} [Rend. Semin. Mat. Univ. Padova 69, 153-168 (1983; Zbl 0522.20022)] have classified infinite groups in which every proper subgroup is finite-by-nilpotent of class \(c\) whereas \textit{B. Bruno} [Boll. Unione Mat. Ital., VI. Ser. B 3, 797-807 (1984; Zbl 0563.20035) and ibid.
Otal, Javier, Peña, Juan Manuel
openaire   +1 more source