Minimality in topological groups and Heisenberg type groups

2007/06/14 by Menachem Shlossberg, Shlossberg, Menachem · 1 citation
Mathematics · #22A05 #54H15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.0706.2160

openalex publication_date 2007/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study relatively minimal subgroups in topological groups. We find, in particular, some natural relatively minimal subgroups in unipotent groups which are defined over "good" rings. By "good" rings we mean archimedean absolute valued (not necessarily associative) division rings. Some of the classical rings which we consider besides the field of reals are the ring of quaternions and the ring of octonions. This way we generalize in part a previous result which was obtained by Dikranjan and Megrelishvili and involved the Heisenberg group.

Cited by

• Generalize Heisenberg Groups and Self-Duality

Related

• Locally Minimal Topological Groups 2
• Notes on non-archimedean topological groups
• Hereditarily minimal topological groups
• Groups with the Minimal Conditions for Subgroups and for Nonabelian Subgroups
• Minimality of the Semidirect Product