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36 relations: Abelian group, Additive group, Affine space, Bijection, Cardinality, Center (group theory), Conjugacy class, Coset enumeration, Coset leader, Disjoint sets, Double coset, Equivalence class, Equivalence relation, Euclidean space, Euclidean vector, Group (mathematics), Heap (mathematics), Index of a subgroup, Infinity, Lagrange's theorem (group theory), Linear code, Linear subspace, Mathematics, Modular arithmetic, Non-measurable set, Normal subgroup, Order (group theory), Parallel (geometry), Partition of a set, Quotient group, Rubik's Cube, Subgroup, Transfer (group theory), Transversal (combinatorics), Vector space, Vitali set.
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.
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Additive group
An additive group is a group of which the group operation is to be thought of as addition in some sense.
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Affine space
In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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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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Center (group theory)
In abstract algebra, the center of a group,, is the set of elements that commute with every element of.
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Conjugacy class
In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
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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.
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Coset leader
In coding theory, a coset leader is a word of minimum weight in any particular coset - that is, a word with the lowest amount of non-zero entries.
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Disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common.
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Double coset
In group theory, a field of mathematics, a double coset is a collection of group elements which are equivalent under the symmetries coming from two subgroups.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
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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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Heap (mathematics)
In abstract algebra, a heap (sometimes also called a groud) is a mathematical generalization of a group.
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Index of a subgroup
In mathematics, specifically group theory, the index of a subgroup H in a group G is the "relative size" of H in G: equivalently, the number of "copies" (cosets) of H that fill up G. For example, if H has index 2 in G, then intuitively half of the elements of G lie in H. The index of H in G is usually denoted |G: H| or or (G:H).
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Infinity
Infinity (symbol) is a concept describing something without any bound or larger than any natural number.
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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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Linear code
In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword.
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Linear subspace
In linear algebra and related fields of mathematics, a linear subspace, also known as a vector subspace, or, in the older literature, a linear manifold, is a vector space that is a subset of some other (higher-dimension) vector space.
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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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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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Non-measurable set
In mathematics, a non-measurable set is a set which cannot be assigned a meaningful "size".
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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.
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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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Parallel (geometry)
In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.
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Partition of a set
In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.
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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.
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Rubik's Cube
Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.
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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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Transfer (group theory)
In the mathematical field of group theory, the transfer defines, given a group G and a subgroup of finite index H, a group homomorphism from G to the abelianization of H. It can be used in conjunction with the Sylow theorems to obtain certain numerical results on the existence of finite simple groups.
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Transversal (combinatorics)
In mathematics, given a family of sets, here called a collection C, a transversal (also called a cross-section) is a set containing exactly one element from each member of the collection.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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Vitali set
In mathematics, a Vitali set is an elementary example of a set of real numbers that is not Lebesgue measurable, found by Giuseppe Vitali.
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Coset in a group, Coset representative, Cosets, Left coset, Right coset.
References
[1] https://en.wikipedia.org/wiki/Coset
