ON INDICES OF SUBNORMAL SUBGROUPS OF FINITE SOLUBLE GROUPS #.

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 ?p( 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. [ABSTRACT FROM AUTHOR]