About coset and normal subgroup

Asked Oct 19 '20 at 12:50

Active Oct 19 '20 at 13:11

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Let $H\le G$ and suppose that $[G:H]$ is the least positive prime factor of $|G|$.

How to show that $H\triangleleft G$?

I am confused in how to establish relation between the number of cosets of $H$ and its normalization. What does the condition "least prime factor" restrict for?

Where should I begin?

edited Oct 19 '20 at 13:11

Shaun

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asked Oct 19 '20 at 12:50

Pump Kin

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Does this answer your question? Normal subgroup of prime index – Mor A. Oct 19 '20 at 13:15
Begin with the construction of a homomorphism from $G$ to $S_p$, whose kernel is contained in $K$, the subgroup of index $p$ (see the duplicate). – Dietrich Burde Oct 19 '20 at 13:22

About coset and normal subgroup

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