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Every finite simple group (that is not cyclic) has even group order, and the group order of every finite simple noncommutative group is doubly even, i.e., divisible by 4 ...

Gaussian brackets are notation published by Gauss in Disquisitiones Arithmeticae and defined by [ ]=1 (1) [a_1]=a_1 (2) [a_1,a_2]=[a_1]a_2+[ ] (3) ...

A theorem that can be stated either in the language of abstract algebraic curves or transcendental extensions. For an abstract algebraic curve, if x and y are nonconstant ...

A Lie algebra over a field of characteristic zero is called semisimple if its Killing form is nondegenerate. The following properties can be proved equivalent for a ...

The Earth-Moon problem is a special case of the empire problem for countries with m=2 disjoint regions, with one region of each country lying on the Earth and one on the Moon ...

A generalization of Turán's theorem to non-complete graphs.

A graphoid consists of a set M of elements together with two collections C and D of nonempty subsets of M, called circuits and cocircuits respectively, such that 1. For any C ...

This problem is NP-complete (Garey and Johnson 1983).

The party problem, also known as the maximum clique problem, asks to find the minimum number of guests that must be invited so that at least m will know each other or at ...

An encoding which provides a bijection between the n^(n-2) labeled trees on n nodes and strings of n-2 integers chosen from an alphabet of the numbers 1 to n. A labeled tree ...