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The number of elements of a group in a given conjugacy class.

For a finite group of h elements with an n_ith dimensional ith irreducible representation, sum_(i)n_i^2=h.

The point of coincidence of P and P^' in Fagnano's theorem.

The order of a finite field is the number of elements it contains.

A system of variables which can be written in the form of Hamilton's equations.

A polynomial function of the elements of a vector x can be uniquely decomposed into a sum of harmonic polynomials times powers of |x|.

Determined the possible values of r and n for which there is an identity of the form (x_1^2+...+x_r^2)(y_1^2+...+y_r^2)=z_1^2+...+z_n^2.

A group having an infinite number of elements. Some infinite groups, such as the integers or rationals, are not continuous groups.

An irreducible representation of a group is a group representation that has no nontrivial invariant subspaces. For example, the orthogonal group O(n) has an irreducible ...

A locally finite space is one for which every point of a given space has a neighborhood that meets only finitely many elements of any cover.