# Homework Help: Counting principles

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1. Oct 13, 2016

### Goomany

1. The problem statement, all variables and given/known data
Suppose that H is a subgroup of G such that whenever H a is not equal to H b.
Then a H not equal to b H.
Prove that g H g ^-H
Contains H.
For all g Is an element of G.

2. Relevant equations

3. The attempt at a solution
I tried the contrapositive position
( sorry, I'm doing this on an iPhone and I can't access latex )

2. Oct 14, 2016

### Staff: Mentor

Are you sure you haven't a mistake in there? $H \subseteq gHg^{-1}H$ for all $g\in G$ means, $H \trianglelefteq G$ is a normal subgroup. What about $G=Sym (3) = \{1,(12),(13),(23),(123),(132)\}$ and $H=\{1,(12)\}$?