(of a group by generators and relations)

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• Group 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… …   Wikipedia

• Group isomorphism problem — In abstract algebra, the group isomorphism problem is the decision problem of determining whether two group presentations present isomorphic groups.The isomorphism problem was identified by Max Dehn in 1911 as one of three fundamental decision… …   Wikipedia

• Symmetric group — Not to be confused with Symmetry group. A Cayley graph of the symmetric group S4 …   Wikipedia

• Combinatorial 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… …   Wikipedia

• Group (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 …   Wikipedia

• Presentation 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.… …   Wikipedia

• Steinberg group (K-theory) — In algebraic K theory, a field of mathematics, the Steinberg group operatorname{St}(A) of a ring A , is the universal central extension of the commutator subgroup of the stable general linear group.It is named after Robert Steinberg, and is… …   Wikipedia

• Fundamental group — In mathematics, the fundamental group is one of the basic concepts of algebraic topology. Associated with every point of a topological space there is a fundamental group that conveys information about the 1 dimensional structure of the portion of …   Wikipedia

• Special 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… …   Wikipedia

• Word (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 …   Wikipedia

• Grothendieck group — In mathematics, the Grothendieck group construction in abstract algebra constructs an abelian group from a commutative monoid in the best possible way. It takes its name from the more general construction in category theory, introduced by… …   Wikipedia