On finite C-tidy groups

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.

کلیدواژه ها:

Finite groups ، cyclicizers ، C-tidy groups