On groups factorized by two subgroups with Chernikov commutants
Copyright policy )On groups factorized by two subgroups with Chernikov commutants
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 minimum condition is almost solvable. The other main result contains the following statement: a locally graded group \(G\) factorized by two subgroups \(A\) and \(B\) with finite subgroups \(A'\) and \(B'\) is almost solvable if at least one of the subgroups \(A\) or \(B\) is periodic.
- National Academy of Sciences of Ukraine Ukraine
- Institute of Mathematics Ukraine
Extensions, wreath products, and other compositions of groups, derived subgroups, Generalizations of solvable and nilpotent groups, Chains and lattices of subgroups, subnormal subgroups, Subgroup theorems; subgroup growth, Chernikov groups, minimum condition, products of subgroups, Products of subgroups of abstract finite groups, Derived series, central series, and generalizations for groups, almost solvable groups, locally graded groups, Local properties of groups
Extensions, wreath products, and other compositions of groups, derived subgroups, Generalizations of solvable and nilpotent groups, Chains and lattices of subgroups, subnormal subgroups, Subgroup theorems; subgroup growth, Chernikov groups, minimum condition, products of subgroups, Products of subgroups of abstract finite groups, Derived series, central series, and generalizations for groups, almost solvable groups, locally graded groups, Local properties of groups
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