On $p$-separability of subgroups of free metabelian groups

Details On $p$-separability of subgroups of free metabelian groups On $p$-separability of subgroups of free metabelian groups

2004-06-13

arxiv.org/abs/math/0406254v1

Mathematics

Group Theory

7 pages

Scientific paper

We prove that every free metabelian non--cyclic group has a finitely generated isolated subgroup which is not separable in the class of nilpotent groups. As a corollary we prove that for every prime number $p$ an arbitrary free metabelian non--cyclic group has a finitely generated $p'$--isolated subgroup which is not $p$--separable.

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