# left coset

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## left coset

[¦left ′käs·ət]
(mathematics)
A left coset of a subgroup H of a group G is a subset of G consisting of all elements of the form ah, where a is a fixed element of G and h is any element of H.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Consequently, clicking on Centralizer triggers the reordering of the group table and coloring of left cosets. The other buttons simply change the set of elements in the left column which are highlighted.
One of the best known applications of group table is given a subgroup H [less than or equal to] G, to organize the table by left cosets of the subgroup and to color the cosets as the Group Calculator does.
is a well-defined binary operation on the set of left cosets of H.
So the natural action of [GAMMA] on the left coset space G/K can be identified with the action of [alpha]([GAMMA]) [subset] Aff(S) on S.
For G/H the set of left cosets of H in G, also denoted G = [[Universal].sub.c[member of]G/H] c, choose once and for all a representative [bar.c] [member of] c.
Dually, the left cosets of B give rise to a right H-action.
Hence, the moment graph is composed of isomorphic graph components indexed by the left cosets of [W.sub.h].
Let H [less than or equal to] G be a subgroup of G, and let X denote the set of left cosets of H in G, i.e.
Shuffles appear in the representation theory of finite groups; the left cosets of the Young Subgroup [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the Symmetric Group [[??].sub.n] (where n = [[summation].sup.k.sub.j=1] [[alpha].sub.j]) correspond exactly to the unique a-shuffles associated with [alpha] = ([[alpha].sub.1], [[alpha].sub.2], ..., [[alpha].sub.k]) (see [Stanley (1999)], page 351).
This is the partition of [S.sub.n] into the left cosets of the subgroup which consists of the permutations of the set {2, 3, ..., n}.
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