# Category: Computational group theory

Schreier vector
In mathematics, especially the field of computational group theory, a Schreier vector is a tool for reducing the time and space complexity required to calculate orbits of a permutation group.
Schreier–Sims algorithm
The Schreier–Sims algorithm is an algorithm in computational group theory, named after the mathematicians Otto Schreier and Charles Sims. This algorithm can find the order of a finite permutation grou
Automatic group
In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph of the group. That is, they can tell if a given
Strong generating set
In abstract algebra, especially in the area of group theory, a strong generating set of a permutation group is a generating set that clearly exhibits the permutation structure as described by a . A st
Knuth–Bendix completion algorithm
The Knuth–Bendix completion algorithm (named after Donald Knuth and Peter Bendix) is a semi-decision algorithm for transforming a set of equations (over terms) into a confluent term rewriting system.
Coset enumeration
In mathematics, coset enumeration is the problem of counting the cosets of a subgroup H of a group G given in terms of a presentation. As a by-product, one obtains a permutation representation for G o
Nielsen transformation
In mathematics, especially in the area of abstract algebra known as combinatorial group theory, Nielsen transformations, named after Jakob Nielsen, are certain automorphisms of a free group which are
Word Processing in Groups
Word Processing in Groups is a monograph in mathematics on the theory of automatic groups; these are a type of abstract algebra whose operations are defined by the behavior of finite automata. The boo
Charles Sims (mathematician)
Charles Coffin Sims (April 14, 1937 – October 23, 2017) was an American mathematician best known for his work in group theory. Together with Donald G. Higman he discovered the Higman–Sims group, one o
Base (group theory)
Let be a finite permutation group acting on a set . A sequence of k distinct elements of is a base for G if the only element of which fixes every pointwise is the identity element of . Bases and stron
Computational group theory
In mathematics, computational group theory is the study ofgroups by means of computers. It is concernedwith designing and analysing algorithms anddata structures to compute information about groups. T
Black box group
In computational group theory, a black box group (black-box group) is a group G whose elements are encoded by bit strings of length N, and group operations are performed by an oracle (the "black box")
Todd–Coxeter algorithm
In group theory, the Todd–Coxeter algorithm, created by J. A. Todd and H. S. M. Coxeter in 1936, is an algorithm for solving the coset enumeration problem. Given a presentation of a group G by generat