A Note on CLT-Groups

Abstract

In this paper, we characterize finite groups G satisfying that, for every prime power divisor p ⁿ of the order of G, there exists a subgroup H of index p ⁿ (of order p ⁿ ) in G such that H is normal or abnormal in G.

Key Words:

• Abnormal subgroups
• Carter subgroups
• CLT-groups
• 𝒩-projector
• Power automorphism

Mathematics Subject Classification (2010):

• 20D10
• 20D20

ACKNOWLEDGMENT

The authors would like to thank the referee for his or her valuable suggestions and useful comments contributed to the final version of this paper. In particular, we thank the referee for helping us to improved the proof of Theorem 3.2.

Notes

Communicated by P. Tiep.