1998/07/21 by Arturo Magidin
Mathematics · #math.GR #msc:08B25 #msc:20E10 #msc:20J99
published as Algebra univers. 48 (2002) 145-150 · Play TeX, 16 pp
arxiv created 1998/07/21 · arxiv updated 2009/11/30
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.