Answer Happy

Then 1 = F.(G)

Posted: Tue Sep 07, 2021 7:27 am

by answerhappygod

Then 1 F G F G F G And This Ascending Sequence Is Called The Upper Nilpotent Series Or Upper Fitting Ser 1 (22.46 KiB) Viewed 67 times

Then 1 = F.(G) <F,(G)<F,(G) <..., and this ascending sequence is called the upper nilpotent series (or upper Fitting series) of G. Prove that G is soluble if and only if F.(G)=G for some n. (iii) Suppose that G is soluble. The least integer n for which F.(G)= G is called the nilpotent length (or Fitting height) of G.