Results 101 to 110 of about 288 (124)

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 \(G\).
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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 \(V\cap H=1\).
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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.
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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
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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.
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On groups factorized by two subgroups with Chernikov commutants

Ukrainian Mathematical Journal, 2000
In the paper infinite groups of the form \(G=AB\) are studied, where the subgroups \(A\) and \(B\) are finite or the derived subgroups \(A'\) and \(B'\) are Chernikov and satisfy some additional restrictions. It is shown that such a group \(G\) in which the subgroups \(A'\) and \(B'\) generate an almost solvable (finite-by-solvable) subgroup with ...
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ON GROUPS WHOSE PROPER SUBGROUPS ARE CHERNIKOV-BY-BAER OR (PERIODIC DIVISIBLE ABELIAN)-BY-BAER

Journal of Algebra and Its Applications, 2013
If 𝔛 is a class of groups, then a group G is called a minimal non-𝔛-group if it is not an 𝔛-group but all of its proper subgroups belong to 𝔛. In this paper we prove that locally graded minimal non-(Chernikov-by-nilpotent)-groups are precisely minimal non-nilpotent-groups without maximal subgroups and that locally graded minimal non-(Chernikov-by-Baer)
ARIKAN, AHMET, Trabelsi, Nadir
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Groups all proper quotient groups of which possess layer-Chernikov properties

Ukrainian Mathematical Journal, 1998
Layer-Chernikov groups were investigated in series of papers, in particular by \textit{D. J. S. Robinson} [J. Algebra 14, 182-193 (1970; Zbl 0186.32204)]. The article under review is dedicated to the investigation of groups all factor-groups of which are layer-Chernikov groups.
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S. N. Chernikov and the development of infinite group theory.

2012
S. N. Černikov has been one of the most prominent and influential scientists of the 20th century working in the field of infinite groups. Černikov's important contributions and some of subsequent (and also recent) applications of his ideas are (shortly) described in this interesting survey article prepared on the occasion of the 100th anniversary of ...
Dixon, M.R., Kirichenko, V.V., Kurdachenko, L.A., Otal, J., Semko, N.N., Shemetkov, L.A., Subbotin, I.Ya.   +6 more
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p-Groups with Černikov Centralizers of Non-Identity Elements of Prime Order

Algebra and Logic, 2001
The author proves the following theorem: Let \(G\) be a \(p\)-group, let \(a\) be an element of prime order \(p\), and let the centralizer \(C_G(a)\) be a Chernikov group. Then either \(G\) is a Chernikov group, or it has a non-locally finite section by a Chernikov subgroup with a unique maximal locally finite subgroup.
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