On Groups with a CC(n)-Subgroup

Abstract

A subgroup H of G is a CC(n)-subgroup of G if |G: H| >n and |C_G(x): C_H(x)| ≤n for each element x ∈ H − {1}. In this article, we study the finite p-groups with a nontrivial CC(p)-subgroup, and the locally nilpotent groups with a nontrivial CC(n)-subgroup.

Key Words:

• Černikov groups
• CC(n)-subgroup
• Divisible abelian p-group
• Locally nilpotent group

2010 Mathematics Subject Classification:

• 20D15
• 20F19

ACKNOWLEDGEMENT

The authors are grateful to the referee for valuable suggestions and comments that lead to significant improvements of this article.

This work was supported by National Natural Science Foundation of China (11001226) and (11071155), Natural Science Foundation Project of CQ(CSTC, 2009BB8111), and Fundamental Research Funds for the Central Universities (XDJK2012B006).

Notes

Communicated by A. Olshanskii.