Posted: November 26th, 2015

Prove that product of primes divides the index of the intersection of two subgroups

Prove that product of primes divides the index of the intersection of two subgroups

Let H and K be subgroups of a finite group G such that [G:H]=p and [G:K]=q where and p and q are distinct primes. Prove that pq divides [G:H intersect K]. I need a step by step proof and a reason for each step using Lagrange’s Theorem

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