ON INDICES OF SUBNORMAL SUBGROUPS OF FINITE SOLUBLE GROUPS

Abstract

All groups considered in this paper are finite soluble groups. Let t _p (G) =  max _H◃◃G {j|p ^j ||| H ^G : H |} and t (G) =  max _{p ∈π( G )} t _p ( G ). In this paper, we study the influence of t ( G ) on the structure of a finite soluble group G . In particular, the bounds of the nilpotent length (derived length, p -length) of a soluble group G with t ( G ) ≤ 2 are found.

Key Words:

• Finite group
• Index
• Soluble group
• Subnormal subgroup

AMS Mathematics Subject Classification (2000):

• 20D10
• 20D35

ACKNOWLEDGMENTS

This work was supported by the NNSF of China (#104711118) and the NNSF of Belarus (# Φ03 − 110).

Notes

^#Communicated by A. Olshanskii.