Orthogonal group

You might be referring to:

• Orthogonal group for the standard dot product: This is probably what you mean if you are working with the real numbers, the rational numbers, or some subfield of the reals, though the concept applies to all fields.
• Orthogonal group for a symmetric bilinear form: A slightly more general notion. This is probably what you mean if you are working with arbitrary fields, particular finite fields and fields of prime characteristic.