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Keywords:
Self-similar group; Cantor set; $p$-adic integers.
Self-similar group; Cantor set; $p$-adic integers.
Summary:
In this paper, we first give several properties with respect to subgroups of self-similar groups in the sense of iterated function system (IFS). We then prove that some subgroups of $p$-adic numbers $\mathbb{Q}_{p}$ are strong self-similar in the sense of IFS.
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