Kernel (algebra) and Symmetric group

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Kernel (algebra) and Symmetric group

Kernel (algebra) vs. Symmetric group

In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective. 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.

Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

Abelian group and Kernel (algebra) · Abelian group and Symmetric group · See more »

Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

Abstract algebra and Kernel (algebra) · Abstract algebra and Symmetric group · See more »

Dimension (vector space)

In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.

Dimension (vector space) and Kernel (algebra) · Dimension (vector space) and Symmetric group · See more »

Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

Field (mathematics) and Kernel (algebra) · Field (mathematics) and Symmetric group · See more »

Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

Function (mathematics) and Kernel (algebra) · Function (mathematics) and Symmetric group · See more »

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

Group (mathematics) and Kernel (algebra) · Group (mathematics) and Symmetric group · See more »

Group homomorphism

In mathematics, given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h: G → H such that for all u and v in G it holds that where the group operation on the left hand side of the equation is that of G and on the right hand side that of H. From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, and it also maps inverses to inverses in the sense that Hence one can say that h "is compatible with the group structure".

Group homomorphism and Kernel (algebra) · Group homomorphism and Symmetric group · See more »

Identity element

In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.

Identity element and Kernel (algebra) · Identity element and Symmetric group · See more »

Module (mathematics)

In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.

Kernel (algebra) and Module (mathematics) · Module (mathematics) and Symmetric group · See more »

Normal subgroup

In abstract algebra, a normal subgroup is a subgroup which is invariant under conjugation by members of the group of which it is a part.

Kernel (algebra) and Normal subgroup · Normal subgroup and Symmetric group · See more »

Quotient group

A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves the group structure.

Kernel (algebra) and Quotient group · Quotient group and Symmetric group · See more »

Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

Kernel (algebra) and Set (mathematics) · Set (mathematics) and Symmetric group · See more »

Singleton (mathematics)

In mathematics, a singleton, also known as a unit set, is a set with exactly one element.

Kernel (algebra) and Singleton (mathematics) · Singleton (mathematics) and Symmetric group · See more »

Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

Kernel (algebra) and Springer Science+Business Media · Springer Science+Business Media and Symmetric group · See more »

Subgroup

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

Kernel (algebra) and Subgroup · Subgroup and Symmetric group · See more »