Year: 2023
Type: preprint
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 $Γ_p$ for $p\geq 3$. This generalizes a result by Sarnak for reciprocal elements in the modular group.
Source: arXiv (Cornell University)
Authors: Das, Debattam, Gongopadhyay, Krishnendu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4383174144