Split orthogonal group of degree two
For characteristic not equal to two, an alternative definition, which gives a conjugate subgroup and hence an isomorphic group, is:
For a finite field , this group is denoted and is termed the orthogonal group of "+" type. It is also denoted where is the size of the field.
Over a finite field
We consider the group where is a field (unique up to isomorphism) of size .