Special Orthogonal Group is Group
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Theorem
Let $k$ be a field.
The $n$th orthogonal group on $k$ is a group.
Proof
A direct corollary of Special Orthogonal Group is Subgroup of Orthogonal 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: $\text{(iv) (c)}$