A generalization of Ramanujan's sum over finite groups

Monu Kadyan, Priya, Sanjay Kumar Singh

Let $G$ be a finite group, and let $x\in G$. Define $[x^G]:=\{y\in G:⟨x^G⟩=⟨y^G⟩\}$, where $⟨x^G⟩$ denotes the normal subgroup o…