Special orthogonal group for the standard dot product

Definition with symbols
Let $$n$$ be a natural number and $$k$$ a field. Then the special orthogonal group of order $$n$$ over the field $$k$$, denoted $$SO(n,k)$$, is defined as the group of all matrices $$A$$ such that $$det(A) = 1$$ and $$AA^t = I$$.

A group is termed a special orthogonal group if it occurs as $$SO(n,k)$$ for some natural number $$n$$ and field $$k$$.

Supergroups

 * Supergroup::Orthogonal group
 * Supergroup::Special affine orthogonal group
 * Supergroup::Affine orthogonal group
 * Supergroup::Special orthogonal similitude group
 * Supergroup::Orthogonal similitude group