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Explicit representation of roots on p-adic solenoids and non-uniqueness of embeddability into rational one-parameter subgroups

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Abstract

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.

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  1. Fachbereich Mathematik, Universität Dortmund, 44221, Dortmund, Germany

    Peter Becker-Kern

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  1. Peter Becker-Kern
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Becker-Kern, P. Explicit representation of roots on p-adic solenoids and non-uniqueness of embeddability into rational one-parameter subgroups. Proc Math Sci 117, 443–455 (2007). https://doi.org/10.1007/s12044-007-0037-6

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