A NOTE ON FINITE C-TIDY GROUPS

Let g be a group and x 2 g. the cyclicizer of x is dened to be the subset cyc(x) = fy 2g j hx; yi is cyclicg. g is said to be a tidy group if cyc(x) is a subgroup for all x 2 g. we call g tobe a c-tidy group if cyc(x) is a cyclic subgroup for all x 2 g n k(g), where k(g) is the intersectionof all the cyclicizers in g. in this note, we classify finite c-tidy groups with k(g) = f1g.