A Bound on the Number of Conjugacy Classes of Non-normal Cyclic Subgroups of a Finite p-Group

چکیده مقاله

Let G be a finite p-group of odd order and let νc(G) be the number of conjugacy classes of non-normal cyclic subgroups of G. In this paper, among other results, we obtain a lower bound for νc(G). More precisely, if |G'| = p^k, for some integer k, then we prove that νc(G) ≥ k.