We assume $\mathbb{K} = \mathbb{R}$. Prove that there exists a surjective group homomorphism $\psi : O _ { 2,1 } \rightarrow \mathbb { Z } / 2 \mathbb { Z } \times \mathbb { Z } / 2 \mathbb { Z }$ whose kernel is $S O _ { 2,1 } ^ { + }$.
We assume $\mathbb{K} = \mathbb{R}$. Prove that there exists a surjective group homomorphism $\psi : O _ { 2,1 } \rightarrow \mathbb { Z } / 2 \mathbb { Z } \times \mathbb { Z } / 2 \mathbb { Z }$ whose kernel is $S O _ { 2,1 } ^ { + }$.