On c-Normal Subgroups of Finite Groups

Abstract

Let G be a finite group. We fix in every noncyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P| and study the structure of G under the assumption that all subgroups H of P with |H| = |D| are c-normal in G.

Key Words:

• Finite group
• c-Normal subgroup
• Normal subgroup
• Saturated formation
• Sylow subgroup

AMS Mathematics Subject Classification (2000):

• 20D10

ACKNOWLEDGMENT

The authors are grateful to the referee helpful suggestions.

Notes

Communicated by A. Yu. Olshanskii.