Explicit Representation of Roots on 𝑝-Adic Solenoids and Non-Uniqueness of Embeddability into Rational One-Parameter Subgroups
This note generalizes known results concerning the existence of roots and embedding one-parameter subgroups on 𝑝-adic solenoids. An explicit representation of the roots leads to the construction of two distinct rational embedding one-parameter subgroups. The results contribute to enlighten the group structure of solenoids and to point out difficulties arising in the context of the embedding problem in probability theory. As a consequence, the uniqueness of embedding of infinitely divisible probability measures on 𝑝-adic solenoids is solved under a certain natural condition.
Volume 130, 2020
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