Totally disconnected locally compact groups with just infinite locally normal subgroups

2021/07/12 by Reid, Colin D.
#20E18 #22D05 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2107.05329

Abstract

We obtain a characterization of totally disconnected, locally compact groups G with the following property: given a locally normal subgroup K of G, then there is an open subgroup of K that is a direct factor of an open subgroup of G. This property is motivated by J. Wilson's structure theory of just infinite groups, and indeed, when G has trivial quasi-centre, the condition turns out to be equivalent to the condition that G is locally isomorphic to a finite direct product of just infinite profinite groups. In the latter situation we obtain some global structural features of G, building on an earlier result of Barnea--Ershov--Weigel and also using tools developed by P.-E. Caprace, G. Willis and the author for studying local structure in totally disconnected locally compact groups.

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