Locally compact groups with few orbits under automorphisms

被引：0

作者：

Stroppel, M ^{[1
]}

机构：

[1] Univ Stuttgart, Inst Geometrie & Topol, D-70550 Stuttgart, Germany

来源：

TOPOLOGY PROCEEDINGS, VOL 26, NO 2, 2001-2002 | 2002年 / 26卷 / 02期

关键词：

locally compact groups; compact groups; automorphisms; orbit; decomposition; topological vector spaces; Heisenberg groups; homogeneous groups; almost homogeneous groups; simply connected nilpotent lie groups; finite simple groups; Suzuki; 2-groups;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The number of orbits under the group of all topological automorphisms was introduced as a new cardinal invariant for topological groups. For locally compact groups, the impact of bounds for this number is investigated. Compact groups with finitely many orbits under automorphisms are pro-finite groups with an open solvable characteristic subgroup; detailed information is obtained for the case of at most 4 orbits. Connected locally compact groups with countably many orbits are simply connected nilpotent Lie groups. Abelian locally compact groups with finitely many orbits under automorphisms are understood quite well. Several open problems are formulated.

引用

页码：819 / 842

页数：24

共 29 条

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