396 Let G be a finite group. (i) Show that if G is soluble and G #1 then F(G) +1. (ii) Define subgroups F (G) recursivel

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396 Let G Be A Finite Group I Show That If G Is Soluble And G 1 Then F G 1 Ii Define Subgroups F G Recursivel 1 (16.16 KiB) Viewed 60 times

396 Let G be a finite group. (i) Show that if G is soluble and G #1 then F(G) +1. (ii) Define subgroups F (G) recursively as follows. Let F.(G)= 1 and, for each positive integer n, let F.(G/F-1(G)= F(G/F - (G)).