Results 141 to 150 of about 9,034,965 (157)

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 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 ...
openaire   +2 more sources

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.
openaire   +1 more source

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
openaire   +2 more sources

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.
openaire   +2 more sources

Semigroups with certain finiteness conditions and Chernikov groups

2019
The main purpose of this short survey is to show how groups of special structure, which are accepted to be called Chernikov groups, appeared in the considerations of semigroups with certain finiteness conditions. A structure of groups with several such conditions has been described (they turned out to be special types of Chernikov groups).
openaire   +2 more sources

Characterization of generalized Chernikov groups among groups with involutions

Mathematical Notes, 1997
V I Senashov
exaly  

Locally finite groups with Chernikov Sylowp-subgroups

Algebra and Logic, 1981
openaire   +3 more sources

Locally finite groups with Chernikov classes of conjugate infinite Abelian subgroups

1988
The conjugacy class of a subgroup H is said to be Chernikov if \(G/core_ G(N_ G(H))\) is Chernikov. The author has shown previously [Izv. Vyssh. Uchebn. Zaved., Mat. 1977, No.4, 95-101 (1977; Zbl 0374.20051)] that in a periodic group G all abelian subgroups have Chernikov conjugacy classes if and only if G is centre-by-Chernikov.
openaire   +2 more sources

Classification of non-isomorphic groups of a certain class of Chernikov 3-groups

В цiй роботi описуються з точнiстю до iзоморфiзму деякi чернiкоськi 3-групи, що є циклiчними розширеннями повних абелевих 3-груп з умовою мiнiмальностi. Нехай ℂ3∞ — адитивна квазiциклiчна 3-група, а ℂn3∞ — зовнiшня пряма сума n екземплярiв квазiциклiчної 3-групи ℂ3∞ для деякого натурального числа n.
openaire   +1 more source