Finite p-Groups and Centralizers of Noncentral Elements

Abstract

Let G be a finite p-group. If |C_G(x): ⟨ x ⟩ | ≤p^k for every noncentral element x of G, then G is called a k − 𝒩𝒞 −p-group. In this article, we give a classification of k − 𝒩𝒞 −p-groups, where k = 1, 2 and p > 2.

Key Words:

• Finite p-group
• k-𝒩𝒞-p-group
• Metacyclic group

AMS Subject Classifications:

• 20D10
• 20D15

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Grant No. 11171243, 10871032), the Natural Science Foundation of Jiangsu Province (No. BK2008156), and Suzhou City Senior Talent Supporting Project.

Notes

Communicated by S. Sehgal.