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Closure with a twist

Index Closure with a twist

Closure with a twist is a property of subsets of an algebraic structure. [1]

28 relations: Algebraic structure, Automorphism, Bit array, Cardinality, Closure (mathematics), Closure with a twist, Cyclic group, Direct product, Element (mathematics), Exclusive or, Generating set of a group, Group (mathematics), Identity element, If and only if, Lagrange's theorem (group theory), Mathematics, Mathematics Magazine, Modular arithmetic, Operation (mathematics), Order (group theory), Permutation, Projection (mathematics), Semidirect product, Set (mathematics), Subgroup, Subset, Sylow theorems, Symmetric group.

Algebraic structure

In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.

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Automorphism

In mathematics, an automorphism is an isomorphism from a mathematical object to itself.

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Bit array

A bit array (also known as bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits.

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Cardinality

In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

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Closure (mathematics)

A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation.

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Closure with a twist

Closure with a twist is a property of subsets of an algebraic structure.

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Cyclic group

In algebra, a cyclic group or monogenous group is a group that is generated by a single element.

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Direct product

In mathematics, one can often define a direct product of objects already known, giving a new one.

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Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

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Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).

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Generating set of a group

In abstract algebra, a generating set of a group is a subset such that every element of the group can be expressed as the combination (under the group operation) of finitely many elements of the subset and their inverses.

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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.

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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.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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Lagrange's theorem (group theory)

Lagrange's theorem, in the mathematics of group theory, states that for any finite group G, the order (number of elements) of every subgroup H of G divides the order of G. The theorem is named after Joseph-Louis Lagrange.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Mathematics Magazine

Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.

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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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Operation (mathematics)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

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Order (group theory)

In group theory, a branch of mathematics, the term order is used in two unrelated senses.

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Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

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Projection (mathematics)

In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent).

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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.

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Set (mathematics)

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

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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 ∗.

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Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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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 Ludwig Sylow (1872) 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.

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References

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

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