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Let 1 =G,G,... 2G, EG be any series of G whose factors are all nilpotent. Prove that G

Posted: Tue Sep 07, 2021 7:28 am

by answerhappygod

Let 1 G G 2g Eg Be Any Series Of G Whose Factors Are All Nilpotent Prove That G F G For Each I 0 1 In 1 (25.01 KiB) Viewed 315 times

Let 1 =G,G,... 2G, EG be any series of G whose factors are all nilpotent. Prove that G <F (G) for each i= 0, 1,...,. In particular, the derived length of G is not less than its nilpotent length. (Hint. Argue by induction on i. Note that by 336, every nilpotent subnormal subgroup of a finite group H is contained in F(H).)