Can you explain me how to show that the PSL(2, 9) is isomorphic to Alt(6)?
then a simple calculation shows that let
be the elements of corresponding to and then:
let (since and have the same presentation.) so
now let be the set of left cosets of define by
where clearly and is a non-trivial homomorphism. since G is simple,
we must have i.e. is an embedding. so G is isomorphic to a subgroup of since
and is the only subgroup of which has order 360, we must have