Isolated circular orders on free products of cyclic groups

In this paper, we construct countably many isolated circular orders on the free products $G = F_{2n} \ast \mathbb{Z}{m_1} \ast \cdots \ast \mathbb{Z}{m_k}$ of cyclic groups. Moreover, we prove that these isolated circular orders are not the automorphic images of the others. By using these isolated circular orders, we also construct countably many isolated left orders on a certain central $\mathbb{Z}$-extension of $G$, which are not the automorphic images of the others.

💡 Research Summary

The paper investigates isolated circular orders and isolated left orders on a broad class of groups obtained as free products of cyclic groups, extending previous results on free groups of even rank and on PSL(2, ℤ).
The authors consider groups of the form
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