# Poincare's Theorem

• September 18th 2009, 09:37 AM
thomas_donald
Poincare's Theorem
Let H1 & H2 be subgroups of G. How can it be shown that if H1 & H2 have finite index in G then so the intersection of H1 & H2.
• September 18th 2009, 12:24 PM
NonCommAlg
Quote:

Originally Posted by thomas_donald

Let H1 & H2 be subgroups of G. How can it be shown that if H1 & H2 have finite index in G then so the intersection of H1 & H2.

Hint (acually the solution!!): $(H_1 \cap H_2)g=H_1g \cap H_2g,$ for all $g \in G.$