presentation (of a group by generators and relations)
1Presentation of a group — In mathematics, one method of defining a group is by a presentation. One specifies a set S of generators so that every element of the group can be written as a product of some of these generators, and a set R of relations among those generators.… …
2Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …
3Absolute presentation of a group — In mathematics, one method of defining a group is by an absolute presentation.B. Neumann, The isomorphism problem for algebraically closed groups, in: Word Problems, Decision Problems, and the Burnside Problem in Group Theory, Amsterdam London… …
4Combinatorial group theory — In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used in geometric topology, the fundamental group of a simplicial complex having in a… …
5Symmetric group — Not to be confused with Symmetry group. A Cayley graph of the symmetric group S4 …
6Presentation of a monoid — In algebra, a presentation of a monoid (or semigroup) is a description of a monoid (or semigroup) in terms of a set Sigma; of generators and a set of relations on the free monoid Sigma; lowast; (or free semigroup Sigma;+) generated by Sigma;. The …
7Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …
8Word (group theory) — In group theory, a word is any written product of group elements and their inverses. For example, if x , y , and z are elements of a group G , then xy , z 1 xzz , and y 1 zxx 1 yz 1 are words in the set { x , y , z }. Words play an important role …
9Special linear group — In mathematics, the special linear group of degree n over a field F is the set of n times; n matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion.This is the normal subgroup of the general… …
10Braid group — In mathematics, the braid group on n strands, denoted by B n , is a certain group which has an intuitive geometrical representation, and in a sense generalizes the symmetric group S n . Here, n is a natural number; if n gt; 1, then B n is an… …
