set of G into disjoint, equal-size subsets called cosets. There are left cosets and right cosets. Cosets (both left and right) have the same number of elements...

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...

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...

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. Sometimes...

the area of mathematics called combinatorial group theory, the Schreier coset graph is a graph associated with a group G, a generating set of G, and a...

subgroup H in a group G is the number of left cosets of H in G, or equivalently, the number of right cosets of H in G. The index is denoted | G : H | {\displaystyle...

correspond to the left cosets G/Ho, and the marked point o corresponds to the coset of the identity. Conversely, given a coset space G/H, it is a homogeneous...

coset enumeration problem. Given a presentation of a group G by generators and relations and a subgroup H of G, the algorithm enumerates the cosets of...

the original group, and the other equivalence classes are precisely the cosets of that normal subgroup. The resulting quotient is written ⁠ G / N {\displaystyle...

left) Each row is a coset with the coset leader in the first column The entry in the i-th row and j-th column is the sum of the i-th coset leader and the j-th...

{\displaystyle H_{3}^{+}=SL(2,\mathbb {C} )/SU(2)} is not a group, but a coset. Given a simple representation ρ {\displaystyle \rho } of the Lie algebra...

In mathematics, the coset construction (or GKO construction) is a method of constructing unitary highest weight representations of the Virasoro algebra...

the same coset for the stabilizer subgroup Gx. Thus, the fiber f−1({y}) of f over any y in G⋅x is contained in such a coset, and every such coset also occurs...

repeated, generating the whole coset S k − 1 τ 1 {\displaystyle S_{k-1}\tau _{1}} , reaching the last permutation in that coset λ k − 1 τ 1 {\displaystyle...

\varphi } if nonempty is a coset bijection from a C {\displaystyle C} -coset of A {\displaystyle A} to an A {\displaystyle A} -coset of C {\displaystyle C}...

left cosets of N {\displaystyle N} where multiplication of any two left cosets g N {\displaystyle gN} and h N {\displaystyle hN} yields the left coset (...

subgroups H and K, with K contained in H. Then the left cosets of H in G are each the union of left cosets of K. Not only that, but translation (on one side)...

Furthermore, every element of G is contained in precisely one left coset of H; the left cosets are the equivalence classes corresponding to the equivalence...

the index [ G : H ] {\displaystyle [G:H]} , defined as the number of left cosets of H {\displaystyle H} in G {\displaystyle G} . Lagrange's theorem—If H...

with c = 3. Di Vecchia et al. (1986) gave a coset construction of the N = 2 superconformal algebras, generalizing the coset constructions of Goddard, Kent & Olive...

{\displaystyle G_{4}=\{1\}} Next he prepared tables for each of the right coset spaces G i + 1 ∖ G i {\displaystyle G_{i+1}\setminus G_{i}} . For each element...

apply to the right cosets of ⁠ H {\displaystyle H} ⁠. The left cosets of H {\displaystyle H} may or may not be the same as its right cosets. If they are (that...

is a Lie group and H is a closed Lie subgroup of G such that the (left) coset space G/H is connected. The group G is called the principal group of the...

{Spec} {\mathcal {O}}} , the set of k-points of GrG is identified with the coset space G ( K ) / G ( O ) {\displaystyle G({\mathcal {K}})/G({\mathcal {O}})}...

right cosets of a fixed subgroup H , {\displaystyle H,} one obtains a related construction, the Schreier coset graph, which is at the basis of coset enumeration...

homomorphism from G to the quotient group G / N, that sends an element g to the coset determined by g. If I is an ideal of a ring R, then there is a canonical...

{\displaystyle X=G/H} be the left coset space and x {\displaystyle x} an arbitrary element in X {\displaystyle X} . Choosing a coset representative g ( x ) ∈ G...

n {\displaystyle n} . Then G {\displaystyle G} acts on the set of left cosets of U {\displaystyle U} in G {\displaystyle G} by left shift: g ( h U ) =...

Such a representation R r , s {\displaystyle {\mathcal {R}}_{r,s}} is a coset of a Verma module by its infinitely many nontrivial submodules. It is unitary...

set difference. The backslash is also sometimes used to denote the right coset space. Especially when describing computer algorithms, it is common to define...