My question is about the induction method. This was in a theorem that I read.(adsbygoogle = window.adsbygoogle || []).push({});

Let H be a normal subgroup of a finite group G. If G satisfies H-some statement then G is solvable.

In the poof I have this.

Let G be a counter example of minimal order. Let N be a proper normal subgroup of G. Since N satisfies the H-some statement then N is solvable by the induction in the order of G.

Here is my question. H may not be a subgroup of N so, how did he apply the induction method.

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# Induction method

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