Wreath product, the Glossary

Table of Contents

1. 31 relations: Acta Scientiarum Mathematicarum, Annales Scientifiques de l'École Normale Supérieure, Binary tree, Dihedral group, Direct product of groups, Direct sum of groups, Encyclopedia of Mathematics, Exponentiation, Factorial, Generalized symmetric group, Graph (discrete mathematics), Group (mathematics), Group action, Group extension, Group isomorphism, Group theory, Hyperoctahedral group, Identity element, Krohn–Rhodes theory, Lamplighter group, London Mathematical Society, Permutation group, Prime number, Rubik's Cube group, Semidirect product, Semigroup, Subgroup, Sylow theorems, Symmetric group, Tree (data structure), Unicode.

2. Binary operations
3. Group products
4. Permutation groups

Acta Scientiarum Mathematicarum

Acta Scientiarum Mathematicarum is a Hungarian mathematical journal published by the János Bolyai Mathematical Institute (University of Szeged).

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Annales Scientifiques de l'École Normale Supérieure

Annales Scientifiques de l'École Normale Supérieure is a French scientific journal of mathematics published by the Société Mathématique de France.

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Binary tree

In computer science, a binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child.

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Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

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Direct product of groups

In mathematics, specifically in group theory, the direct product is an operation that takes two groups and and constructs a new group, usually denoted. Wreath product and direct product of groups are group products.

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Direct sum of groups

In mathematics, a group G is called the direct sumHomology.

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Encyclopedia of Mathematics

The Encyclopedia of Mathematics (also EOM and formerly Encyclopaedia of Mathematics) is a large reference work in mathematics.

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Exponentiation

In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power. Wreath product and exponentiation are binary operations.

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Factorial

In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &.

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Generalized symmetric group

In mathematics, the generalized symmetric group is the wreath product S(m,n). Wreath product and generalized symmetric group are permutation groups.

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Graph (discrete mathematics)

In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related".

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Group (mathematics)

In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.

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Group action

In mathematics, many sets of transformations form a group under function composition; for example, the rotations around a point in the plane.

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Group extension

In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group.

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Group isomorphism

In abstract algebra, a group isomorphism is a function between two groups that sets up a bijection between the elements of the groups in a way that respects the given group operations.

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Group theory

In abstract algebra, group theory studies the algebraic structures known as groups.

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Hyperoctahedral group

In mathematics, a hyperoctahedral group is an important type of group that can be realized as the group of symmetries of a hypercube or of a cross-polytope.

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Identity element

In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. Wreath product and identity element are binary operations.

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Krohn–Rhodes theory

In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components.

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Lamplighter group

In mathematics, the lamplighter group L of group theory is the restricted wreath product \mathbf_2 \wr \mathbf Z.

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London Mathematical Society

The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical Society and the Operational Research Society (ORS).

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Permutation group

In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). Wreath product and permutation group are permutation groups.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.

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Rubik's Cube group

The Rubik's Cube group is a group (G, \cdot) that represents the structure of the Rubik's Cube mechanical puzzle. Wreath product and Rubik's Cube group are permutation groups.

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Semidirect product

In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. Wreath product and semidirect product are group products.

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Semigroup

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it.

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Subgroup

In group theory, a branch of mathematics, given a group under a binary operation ∗, a subset of is called a subgroup of if also forms a group under the operation ∗.

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Sylow theorems

In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow that give detailed information about the number of subgroups of fixed order that a given finite group contains.

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Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. Wreath product and symmetric group are permutation groups.

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Tree (data structure)

In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes.

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Unicode

Unicode, formally The Unicode Standard, is a text encoding standard maintained by the Unicode Consortium designed to support the use of text in all of the world's writing systems that can be digitized.

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See also

Binary operations

• Absorbing element
• Barrel shifter
• Binary operation
• Blaschke sum
• Cap product
• Circular convolution
• Commutator
• Composition of relations
• Courant bracket
• Cup product
• DE-9IM
• Demonic composition
• Elvis operator
• Exponentiation
• Ext functor
• Function composition
• Icosian calculus
• Identity element
• Inverse element
• Iterated binary operation
• Join and meet
• Light's associativity test
• Logic alphabet
• Logical connectives
• Logical consequence
• Lulu smoothing
• Magma (algebra)
• Mean operation
• Minkowski addition
• Modular multiplicative inverse
• Null coalescing operator
• Operations on numbers
• Relational operator
• Tor functor
• Wreath product

Group products

• Direct product of groups
• Free product
• Product of group subsets
• Semidirect product
• Wreath product

Permutation groups

• Affine symmetric group
• Alternating group
• Automorphisms of the symmetric and alternating groups
• Base (group theory)
• Block (permutation group theory)
• Burnside ring
• Cayley graph
• Covering groups of the alternating and symmetric groups
• Faro shuffle
• Frobenius group
• Gassmann triple
• Generalized symmetric group
• Hall's universal group
• Jordan's theorem (symmetric group)
• Jucys–Murphy element
• List of transitive finite linear groups
• Multiply transitive group action
• O'Nan–Scott theorem
• Parker vector
• Permutation group
• Permutation representation
• Primitive permutation group
• Rubik's Cube group
• Schreier vector
• Schreier–Sims algorithm
• Sims conjecture
• Strong generating set
• Symmetric group
• System of imprimitivity
• Wreath product
• Young subgroup
• Zassenhaus group

References

[1] https://en.wikipedia.org/wiki/Wreath_product

Also known as Regular wreath product, Restricted wreath product, Unrestricted wreath product, Wreathed product, .