1. An element x of a set E is said to be invariant with respect to a group G of mappings acting on E if g(x )=x for all g in G.

2. A subset F of a set E is said to be invariant with respect to a group G of mappings acting on E if g(x ) is in F for all x in F and all g in G.

3. For an algebraic equation, an expression involving the coefficients that remains unchanged under a rotation or translation of the coordinate axes in the cartesian space whose coordinates are the unknown quantities.