This sequence splits by taking any matrix with determinant , for example the diagonal matrix If is odd, the negative identity matrix is in but not in and thus the group splits as an internal direct product . However, if is even, is already in , does not split, and in general is a non-trivial group extension.
This sequence splits by taking any matrix with determinant , for example the diagonal matrix If is odd the negative identity matrix is in but not in and thus the group splits as an internal direct product . However, if is even, is already in , does not split, and in general is a non-trivial group extension.