Can you explain me how to show that the PSL(2, 9) is isomorphic to Alt(6)?

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- Jul 3rd 2008, 12:43 AMdimukPsl(2, 9)
Can you explain me how to show that the PSL(2, 9) is isomorphic to Alt(6)?

- Jul 3rd 2008, 03:15 AMNonCommAlg
clearly we have where now consider these two elements of

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 - Jul 3rd 2008, 03:33 AMdimukPsl(2,9)
Thank you. I got the idea.

- Jul 3rd 2008, 10:16 AMThePerfectHacker
- Jul 4th 2008, 01:29 AMNonCommAlg