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A p-element x of a group G is semisimple if E(C_G(x))!=1, where E(H) is the commuting product of all components of H and C_G(x) is the centralizer of G.

The vector triple product identity Ax(BxC)=B(A·C)-C(A·B). This identity can be generalized to n dimensions,

A representation of a group G is a group action of G on a vector space V by invertible linear maps. For example, the group of two elements Z_2={0,1} has a representation phi ...

A dozen dozen, also called a gross. 144 is a square number and a sum-product number.

Given a set of objects S, a binary relation is a subset of the Cartesian product S tensor S.

The intersection product for classes of rational equivalence between cycles on an algebraic variety.

The geometry of the Lie group R semidirect product with R^2, where R acts on R^2 by (t,(x,y))->(e^tx,e^(-t)y).

A bundle or fiber bundle is trivial if it is isomorphic to the cross product of the base space and a fiber.

A similar construction can be done by initially erecting a square internally on the side BC. This leads to the A^--inscribed square. The triangle DeltaX^-Y^-Z^- of centers of ...

The first Napoleon point N is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding inner Napoleon ...