# Split orthogonal group of degree two

From Groupprops

## Contents

## Definition

Suppose is a field. The **split orthogonal group of degree two** over is defined as the subgroup of the general linear group of degree two over given as follows:

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.

## Arithmetic functions

### Over a finite field

We consider the group where is a field (unique up to isomorphism) of size .

Function | Value | Similar groups | Explanation |
---|---|---|---|

order |

## Particular cases

### Over a finite field

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