/sci/ - Science & Math

>>12519670
I was wondering if it would fail for finite groups. Let's say we have a prime number p dividing the order of G, and let H be any subset of G. Let [math]O^p(G)[/math] be the normal subgroup of G generated by the elements whose order is not divisible by p, and let [math]K = O^p(G) \cap H[/math]. I've been trying to show that K need not be normal, but approaching it from the direction of G/K is way over my skills.