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In general, groups are not Abelian. However, there is always a group homomorphism h:G->G^' to an Abelian group, and this homomorphism is called Abelianization. The ...

The inequality sinAsinBsinC<=((3sqrt(3))/(2pi))^3ABC, where A, B, and C are the vertex angles of a triangle. The maximum is reached for an equilateral triangle (and therefore ...

A series sum_(n)u_n is said to converge absolutely if the series sum_(n)|u_n| converges, where |u_n| denotes the absolute value. If a series is absolutely convergent, then ...

Given a field F and an extension field K superset= F, an element alpha in K is called algebraic over F if it is a root of some nonzero polynomial with coefficients in F. ...

An angle bracket is the combination of a bra and ket (bra+ket = bracket) which represents the inner product of two functions or vectors (or 1-forms), <f|g>=intf(x)g^|(x)dx in ...

An Artin L-function over the rationals Q encodes in a generating function information about how an irreducible monic polynomial over Z factors when reduced modulo each prime. ...

The wreathed product of the monster group by Z_2. The bimonster is a quotient of the Coxeter group with the above Coxeter-Dynkin diagram. This had been conjectured by Conway, ...

The term "Cartesian" is used to refer to anything that derives from René Descartes' conception of geometry (1637), which is based on the representation of points in the plane ...

The problem of finding the number of different ways in which a product of n different ordered factors can be calculated by pairs (i.e., the number of binary bracketings of n ...

Cohomology is an invariant of a topological space, formally "dual" to homology, and so it detects "holes" in a space. Cohomology has more algebraic structure than homology, ...