Dominions in varieties of nilpotent groups

1998/04/30 by Arturo Magidin
Mathematics · #math.GR #msc:08B25 #msc:20F18 #msc:20F45 #msc:20E10 #msc:20F12

paper · pdf

published as Comm. Alg. 28(3) pp. 1241-1270 (2000) · 30 pages, plain TeX. Added results on metabelian groups, corrected typos. Final version

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

Abstract

We investigate the concept of dominion (in the sense of Isbell) in several varieties of nilpotent groups. We obtain a full description of dominions in the variety of nilpotent groups of class at most two. Then we look at the behavior of dominions of subgroups of groups in \cal N₂ when taken in the context of \cal N_c with c>2. Finally we establish the existence of nontrivial dominions in the category of all nilpotent groups.

Related

• Dominions in finitely generated nilpotent groups
• A generalized argument for dominions in varieties of groups
• Dominions in decomposable varieties
• Dominions in varieties generated by simple groups
• Amalgams of nilpotent groups of class two