- #1
naele
- 202
- 1
Homework Statement
Is there an isomorphism between
[tex]
O(2n)\simeq SO(2n)\times \mathbb{Z}_2
[/tex]
[tex]
O(2n+1)\simeq SO(2n+1)\times \mathbb{Z}_2
[/tex]
Homework Equations
First isomorphism theorem
The Attempt at a Solution
I think, if I can show a homomorphism between [itex]SO(2n)\times\mathbb{Z}_2[/itex] and O(2n) then showing whether the kernel is just the identity or not shouldn't be too difficult. But, this is my first time showing a homomorphism with a product of two groups, so I'm unsure how to proceed, namely how do I show that [itex]\phi(S_1S_2)=\phi(S_1)\phi(S_2)[/itex]