5 research outputs found
On strongly just infinite profinite branch groups
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.Comment: Typos and a minor error correcte