Decomposition of locally compact coset spaces

2021/06/29 by Reid, Colin D.
#22D05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2106.15180

Abstract

In a previous article by the author and P. Wesolek, it was shown that a compactly generated locally compact group G admits a finite normal series (G_i) in which the factors are compact, discrete or irreducible in the sense that no closed normal subgroup of G lies properly between G_i-1 and G_i. In the present article, we generalize this series to an analogous decomposition of the coset space G/H with respect to closed subgroups, where G is locally compact and H is compactly generated. This time, the irreducible factors are coset spaces G_i/G_i-1 where G_i is compactly generated and there is no closed subgroup properly between G_i-1 and G_i. Such irreducible coset spaces can be thought of as a generalization of primitive actions of compactly generated locally compact groups; we establish some basic properties and discuss some sources of examples.

Related

• The essentially chief series of a compactly generated locally compact group
• Distal actions on coset spaces in totally disconnected, locally compact groups
• Equivariant extension properties of coset spaces of locally compact groups and approximate slices
• Fibrations and coset spaces for locally compact groups
• Spaces of closed subgroups of locally compact groups