Generalized Rigid Metabelian Groups
We study the generalized rigid groups (r-groups), in the metabelian case in more detail. The periodic r-groups are described. We prove that each divisible metabelian r-group decomposes as a semidirect product of two abelian subgroups, each metabelian r-group independently embeds into a divisible metabelian r-group, and the intersection of each collection of divisible subgroups of a metabelian r-group is divisible too.
Keywordssoluble group metabelian group divisible group
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