On finite C-tidy groups

Abstract

A group $G$ is said to be a C-tidy group if for every element $x in G setminus K(G)$‎, ‎the set $Cyc(x)=lbrace y in G mid langle x‎, ‎y rangle ; {rm is ; cyclic} rbrace$ is a cyclic subgroup of $G$‎, ‎where $K(G)=underset{x in G}bigcap Cyc(x)$‎. ‎In this short note we determine the structure of finite C-tidy groups‎.