/sci/ - Science & Math

>>11442903
[math]P[/math] is a Sylow p-subgroup. Any isomorphism [math]\theta [/math] would necessarily induce an isomorphism onto its image. Thus, the image would also be a Sylow p-subgroup of [math]G[/math]
But any two Sylow p-subgroups are conjugate, and since [math]P[/math] is normal, it isn't conjugate to anything else.

This is probably wrong, my group theory is rusty.

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