- #1

Bashyboy

- 1,421

- 5

## Homework Statement

Suppose that ##H## and ##K## are subgroups of finite index in the (possibly infinite) group ##G## with ##|G : H|m## and ##|G:K|=n##. Prove that ##lcm(m,n) \le |G : H \cap K | < mn##.

## Homework Equations

## The Attempt at a Solution

I was able to get the upper bound on ##|G : H \cap K|##, but am having difficulty showing that the lower bound is ##lcm(m,n)##. I tried showing that ##m## and ##n## both divide ##|G : H \cap K |##, but I couldn't get anywhere. I could use some hints!