Dimension and randomness in groups acting on rooted trees
Dimension and randomness in groups acting on rooted trees
We explore the structure of the<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"><mml:semantics><mml:mi>p</mml:mi><mml:annotation encoding="application/x-tex">p</mml:annotation></mml:semantics></mml:math></inline-formula>-adic automorphism group<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Y"><mml:semantics><mml:mi>Y</mml:mi><mml:annotation encoding="application/x-tex">Y</mml:annotation></mml:semantics></mml:math></inline-formula>of the infinite rooted regular tree. We determine the asymptotic order of a typical element, answering an old question of Turán. We initiate the study of a general dimension theory of groups acting on …