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MiS Preprint

Some remarks on the entropy for algebraic actions of amenable groups

Nhân Phú Chung and Andreas Thom


In this short note we study the entropy for algebraic actions of certain amenable groups. The possible values for this entropy are studied. Various fundamental results about certain classes of amenable groups are reproved using elementary arguments and the entropy invariant. We provide a natural decomposition of the entropy into summands contributed by individual primes and a summand corresponding to infinity. These results extend previous work by Lind and Ward on p-adic entropy.

MSC Codes:
28D20, 37B40, 20J06
entropy, Torsion, Amenable groups, Algebraic actions

Related publications

2015 Repository Open Access
Nhan Phú Chung and Andreas Berthold Thom

Some remarks on the entropy for algebraic actions of amenable groups

In: Transactions of the American Mathematical Society, 367 (2015) 12, pp. 8579-8595