I'm really looking for a "cute" way of showing that $SL_2(\mathbb{F}_5)$ is a double cover of $A_5$. The sort of action I am looking for is something like the action of $GL_2(\mathbb{F}_3)$ on $\mathbb{P}^1(\mathbb{F}_3)$, which shows $GL_2(\mathbb{F}_3)$ is a double cover of $S_4$. Now that's cute.
Is there a "natural" transitive action of $SL_2(\mathbb{F}_5)$ on a set with 5 elements?
5
$\begingroup$
group-theory
matrices
finite-groups
permutations
-
1Here's a related thread you may be interested in: http://math.stackexchange.com/q/93762/ – 2012-03-29