Let G be a group, and let H 0 e H 1 H n G be a composition series for G Let N be a normal subgroup of G, and let G G N be the canonical map Show that the distinct groups among H i for i 0, , n, form a composition series for G N ...

First we show that is well defined Let h i n 1 and h i n 2 be the same elements of H i N Then ...

Let G be a group, and let H 0 = {e} < H 1 < <

Question:

Let G be a group, and let H₀ = {e} < H₁ < ··· < H_n = G be a composition series for G. Let N be a normal subgroup of G, and let γ : G → G/N be the canonical map. Show that the distinct groups among γ[H_i] for i = 0, ··· , n, form a composition series for G/N.

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