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The group direct sum of a sequence {G_n}_(n=0)^infty of groups G_n is the set of all sequences {g_n}_(n=0)^infty, where each g_n is an element of G_n, and g_n is equal to the ...

Formulas obtained from differentiating Newton's forward difference formula, where R_n^'=h^nf^((n+1))(xi)d/(dp)(p; n+1)+h^(n+1)(p; n+1)d/(dx)f^((n+1))(xi), (n; k) is a ...

A type of mathematical result which is considered by most logicians as more natural than the metamathematical incompleteness results first discovered by Gödel. Finite ...

The projective special orthogonal group PSO_n(q) is the group obtained from the special orthogonal group SO_n(q) on factoring by the scalar matrices contained in that group. ...

The projective special unitary group PSU_n(q) is the group obtained from the special unitary group SU_n(q) on factoring by the scalar matrices contained in that group. ...

An algorithm for determining the order of an elliptic curve E/F_p over the finite field F_p.

Every closed three-manifold with finite fundamental group has a metric of constant positive scalar curvature, and hence is homeomorphic to a quotient S^3/Gamma, where Gamma ...

The trivial group, denoted E or <e>, sometimes also called the identity group, is the unique (up to isomorphism) group containing exactly one element e, the identity element. ...

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a ...