Absolutely closed nil-2 groups

1998/03/31 by Arturo Magidin
Mathematics · #math.GR #msc:20E06 #msc:20F18

paper · pdf

published as Algebra Universalis 42 (1-2) pp. 61-77 (1999) · 21 pages plain TeX. Final version, with full classification

arxiv created 1999/05/13 · arxiv updated 2009/11/30

Abstract

Using the description of dominions in the variety of nilpotent groups of class at most two, we give a characterization of which groups are absolutely closed in this variety. We use the general result to derive an easier characterization for some subclasses; e.g. an abelian group G is absolutely closed in \cal N₂ if and only if G/pG is cyclic for every prime p.

Related

• Dominions in varieties of nilpotent groups
• On finite totally k-closed groups
• Dominions in finitely generated nilpotent groups
• A Class of Groups in Which All Unconditionally Closed Sets are Algebraic
• On totally k-closed nilpotent groups