Groups all proper quotient groups of which possess layer-Chernikov properties
Copyright policy )Groups all proper quotient groups of which possess layer-Chernikov properties
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. The main result of the paper is a description of the types of solvable groups of that class. Among them are almost Abelian minimax groups all proper quotients of which are Chernikov, and locally cyclic groups without torsion. There are several types of groups \(G\) which are semidirect products \(G=A\leftthreetimes E\). Both factors are determined in the description of these types.
FC-groups and their generalizations, Solvable groups, supersolvable groups, Subgroup theorems; subgroup growth, Other classes of groups defined by subgroup chains, locally cyclic groups, layer-Chernikov groups, almost Abelian minimax groups, FC-groups, Periodic groups; locally finite groups, periodic groups, Local properties of groups, Residual properties and generalizations; residually finite groups, solvable groups
FC-groups and their generalizations, Solvable groups, supersolvable groups, Subgroup theorems; subgroup growth, Other classes of groups defined by subgroup chains, locally cyclic groups, layer-Chernikov groups, almost Abelian minimax groups, FC-groups, Periodic groups; locally finite groups, periodic groups, Local properties of groups, Residual properties and generalizations; residually finite groups, solvable groups
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