On the product of an abelian group and a nilpotent group
Copyright policy )On the product of an abelian group and a nilpotent group
Summary: The structure of the product of an Abelian group by a nilpotent group is studied. Conditions for the existence of a normal subgroup in one of the factors are given. These conditions generalize the known results on the product of two Abelian groups. The statements obtained are used to describe the structure of the product of an infinite cyclic subgroup by a periodic nilpotent subgroup.
infinite cyclic subgroups, normal subgroups, Extensions, wreath products, and other compositions of groups, General structure theorems for groups, Nilpotent groups, Subgroup theorems; subgroup growth, products of groups, nilpotent groups, Abelian groups
infinite cyclic subgroups, normal subgroups, Extensions, wreath products, and other compositions of groups, General structure theorems for groups, Nilpotent groups, Subgroup theorems; subgroup growth, products of groups, nilpotent groups, Abelian groups
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