2015/10/06 by François Le Maître, Maître, François Le, Phillip Wesolek +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Holomorphic and Operator Theory #Logic (math.LO) #math.GR #math.LO
paper · pdf · doi:10.48550/arxiv.1510.01689
Typos and a minor error corrected
openalex publication_date 2015/10/06 · arxiv created 2016/01/31 · arxiv updated 2016/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.