On strongly just infinite profinite branch groups - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Group Theory Année : 2017

On strongly just infinite profinite branch groups

Résumé

Abstract For profinite branch groups, we first demonstrate the equivalence of the Bergman property, uncountable cofinality, Cayley boundedness, the countable index property, and the condition that every non-trivial normal subgroup is open; compact groups enjoying the last condition are called strongly just infinite. For strongly just infinite profinite branch groups with mild additional assumptions, we verify the invariant automatic continuity property and the locally compact automatic continuity property. Examples are then presented, including the profinite completion of the first Grigorchuk group. As an application, we show that many Burger–Mozes universal simple groups enjoy several automatic continuity properties.

Dates et versions

hal-04460700 , version 1 (15-02-2024)

Identifiants

Citer

François Le Maître, Phillip Wesolek. On strongly just infinite profinite branch groups. Journal of Group Theory, 2017, 20 (1), pp.1-32. ⟨10.1515/jgth-2016-0022⟩. ⟨hal-04460700⟩
6 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More