Orthogonal Group is Group

Theorem

Let $k$ be a field.

The $n$th orthogonal group on $k$ is a group.

Proof

A direct corollary of Orthogonal Group is Subgroup of General Linear Group.

$\blacksquare$

Sources

• 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 3$: Examples of Infinite Groups: $\text{(iv) (b)}$