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arXiv · 2307.00496

Reciprocity in the Hecke Groups

Debattam Das·Krishnendu Gongopadhyay
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Abstract

An element $g$ in a group $G$ is called \emph{reciprocal} if there exists $h \in G$ such that $g^{-1}=hgh^{-1}$. The reciprocal elements are also known as `real elements' or `reversible elements' in the literature. We classify the reciprocal elements and parametrize the reciprocal classes in the Hecke groups $\Gamma_p$ for $p\geq 3$. This generalizes a result by Sarnak for reciprocal elements in the modular group.

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Debattam Das, Krishnendu Gongopadhyay. 2023-07-02. Reciprocity in the Hecke Groups. https://arxiv.org/abs/2307.00496

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