Let [tex]p[/tex] be a prime, [tex]G[/tex] a finite group, and [tex]P[/tex] a [tex]p[/tex]-Sylow subgroup of [tex]G[/tex]. Let [tex]M[/tex] be any subgroup of [tex]G[/tex] which contains [tex]N_G(P)[/tex]. Prove that [tex][G:M]\equiv 1[/tex] (mod [tex]p[/tex]). (Hint: look carefully at Sylow's Theorems.)(adsbygoogle = window.adsbygoogle || []).push({});

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# P-Sylow subgroup congruence

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