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During his work devoted to Coxeter's friezes, M. Cuntz initiated the study ofthe notion of $\lambda$-quiddity and raised the problem of the study of thisover some subsets of $\mathbb{C}$. The objective of this text is to bring somenew elements of response in the case of some cyclic subgroups of($\mathbb{C},+$) generated by an algebraic number. In particular, we will studythe cases of subgroups generated by $a+b\sqrt{k}$.

$\lambda$-quiddity and subgroups generated by an algebraic number