A CHARACTERIZATION OF INFINITE ČERNIKOV GROUPS THAT ARE NOT FINITE EXTENSIONS OF QUASI-CYCLIC GROUPS
Copyright policy )A CHARACTERIZATION OF INFINITE ČERNIKOV GROUPS THAT ARE NOT FINITE EXTENSIONS OF QUASI-CYCLIC GROUPS
We characterize the groups named in the title. Our main result is as follows: an infinite locally finite group G that is not a finite extension of a quasi-cyclic group is a Cernikov group if and only if it has a subgroup H of finite index whose holomorph contains a copy of the four-group in such a way that the centralizer in H of each of its three involutions is a Cernikov group. Bibliography: 17 titles.
minimal condition on subgroups, Chains and lattices of subgroups, subnormal subgroups, Periodic groups; locally finite groups, Subgroup theorems; subgroup growth, Chernikov groups, abelian normal subgroups of finite index, locally finite groups, Local properties of groups
minimal condition on subgroups, Chains and lattices of subgroups, subnormal subgroups, Periodic groups; locally finite groups, Subgroup theorems; subgroup growth, Chernikov groups, abelian normal subgroups of finite index, locally finite groups, Local properties of groups
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