Results 111 to 120 of about 2,730 (156)

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

Characterization of a certain class of chernikov groups

Algebra and Logic, 1987
See the review in Zbl 0654.20035.
Popov, A. M., Shunkov, V. P.
openaire   +2 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

Chernikov p-groups and integral p-adic representations of finite groups

Ukrainian Mathematical Journal, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gudivok, P. M., Vashchuk, F. G., Drobotenko, V. S.   +2 more
openaire   +1 more source

Central-by-Chernikov groups are compact co-Chernikov CC-groups

Annali di Matematica Pura ed Applicata, 2003
Generalizing cofinite groups, M.R. Dixon [Glasgow Math. J. 23 (1982)] has shown how a residually Chernikov group can be made into a topological space, which is called a co-Chernikov group. A co-Chernikov group can be embedded in a compact co-Chernikov group, its pro-Chernikov completion.
openaire   +1 more source

Characterization of groups with generalized chernikov periodic part

Mathematical Notes, 2000
A Chernikov group is a finite extension of a direct product of finitely many quasicyclic groups. A generalized Chernikov group \(G\) is an extension of a direct product \(A\) of quasicyclic \(p\)-groups with finitely many factors for each prime \(p\) by a locally normal group \(B\), where each element of \(G\) is element-wise permutable with all but a ...
openaire   +2 more sources

On groups whose all proper subgroups have Chernikov derived subgroups

Journal of Mathematical Sciences, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Semko, Nikolai N., Yarovaya, Oksana A.
openaire   +1 more source

Groups all proper quotient groups of which have Chernikov conjugacy classes

Ukrainian Mathematical Journal, 2000
Groups with Chernikov classes of conjugated elements (CC-groups) are a generalization of FC-groups and they can be defined as groups with Chernikov factor groups \(G/C_G(x)^G\) for all \(x\in G\) (as usual, \(C_G(x)^G\) denotes the normal closure of \(C_G(x)\) in \(G\)).
Kurdachenko, L. A., Otal, J.
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