Abstract
We obtain some global features of totally disconnected locally compact (t.d.l.c.) groups G that are locally isomorphic to a just infinite profinite group, 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 t.d.l.c. groups. The approach uses the following property of just infinite profinite groups, essentially due to Wilson: 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 is a local property of t.d.l.c. groups and we obtain a characterization of the local isomorphism types of t.d.l.c. groups that have it.
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Acknowledgements
This article started as an offshoot of the project with Pierre-Emmanuel Caprace and George Willis that led to [5], [6] and [7], and was also partly developed during research visits to Alejandra Garrido and John Wilson at Oxford, and to Yiftach Barnea at RHUL. I thank all of them for their hospitality and for very helpful discussions. I also thank the referee, whose recommendations have led to a number of improvements to the presentation.
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Research supported by ARC grant FL170100032.
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Reid, C.D. Totally disconnected locally compact groups with just infinite locally normal subgroups. Isr. J. Math. 259, 461–502 (2024). https://doi.org/10.1007/s11856-023-2490-z
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DOI: https://doi.org/10.1007/s11856-023-2490-z