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A nonassociative algebra obeyed by objects such as the Lie bracket and Poisson bracket. Elements f, g, and h of a Lie algebra satisfy [f,f]=0 (1) [f+g,h]=[f,h]+[g,h], (2) and ...

There are two definitions of a metacyclic group. 1. A metacyclic group is a group G such that both its commutator subgroup G^' and the quotient group G/G^' are cyclic (Rose ...

Modular arithmetic is the arithmetic of congruences, sometimes known informally as "clock arithmetic." In modular arithmetic, numbers "wrap around" upon reaching a given ...

Noncommutative topology is a recent program having important and deep applications in several branches of mathematics and mathematical physics. Because every commutative ...

O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...

Let G be a Lie group and let rho be a group representation of G on C^n (for some natural number n), which is continuous in the sense that the function G×C^n->C^n defined by ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

A set A of integers is said to be one-one reducible to a set B (A<<_1B) if there is a one-one recursive function f such that for every x, x in A=>f(x) in B (1) and f(x) in ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

A short exact sequence of groups 0-->A-->B-->C-->0 (1) is called split if it essentially presents B as the direct sum of the groups A and C. More precisely, one can construct ...