Nonsurjective epimorphisms in decomposable varieties of groups

Details Nonsurjective epimorphisms in decomposable varieties of groups Nonsurjective epimorphisms in decomposable varieties of groups

1998-07-21

arxiv.org/abs/math/9807117v1

Algebra univers. 48 (2002) 145-150

Mathematics

Group Theory

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Scientific paper

A full characterization of when a subgroup $H$ of a group $G$ in a varietal product ${\cal NQ}$ is epimorphically embedded in $G$ (in the variety ${\cal NQ}$) is given. From this, a result of S.~McKay is derived, which states that if ${\cal NQ}$ has instances of nonsurjective epimorphisms, then ${\cal N}$ also has instances of nonsurjective epimorphisms. Two partial converses to McKay's result are also given: when~$G$ is a finite nonabelian simple group; and when~$G$ is finite and ${\cal Q}$ is a product of varieties of nilpotent groups, each of which contains the infinite cyclic group.

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