Definitions for coset
coset

WiktionaryRate this definition:0.0 / 0 votes

1. cosetnoun

   Of a subgroup, a copy of that subgroup multiplied by some element from the parent group.

WikipediaRate this definition:0.0 / 0 votes

1. Coset

   In mathematics, specifically group theory, a subgroup H of a group G may be used to decompose the underlying 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 (cardinality) as does H. Furthermore, H itself is both a left coset and a right coset. The number of left cosets of H in G is equal to the number of right cosets of H in G. This common value is called the index of H in G and is usually denoted by [G : H]. Cosets are a basic tool in the study of groups; for example, they play a central role in Lagrange's theorem that states that for any finite group G, the number of elements of every subgroup H of G divides the number of elements of G. Cosets of a particular type of subgroup (a normal subgroup) can be used as the elements of another group called a quotient group or factor group. Cosets also appear in other areas of mathematics such as vector spaces and error-correcting codes.

WikidataRate this definition:0.0 / 0 votes

1. Coset

   In mathematics, if G is a group, and H is a subgroup of G, and g is an element of G, then Only when H is normal will the right and left cosets of H coincide, which is one definition of normality of a subgroup. Although derived from a subgroup, cosets are not usually themselves subgroups of G, only subsets. A coset is a left or right coset of some subgroup in G. Since Hg = g, the right coset Hg and the left coset g are the same. Hence it is not meaningful to speak of a coset as being left or right unless one first specifies the underlying subgroup. In other words: a right coset of one subgroup equals a left coset of a different subgroup. If the left cosets and right cosets are the same then H is a normal subgroup and the cosets form a group called the quotient group. The map gH→−1=Hg−1 defines a bijection between the left cosets and the right cosets of H, so the number of left cosets is equal to the number of right cosets. The common value is called the index of H in G. For abelian groups, left cosets and right cosets are always the same. If the group operation is written additively then the notation used changes to g+H or H+g.

Anagrams for coset »

1. cotes

2. ScotE

3. estoc

How to pronounce coset?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say coset in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of coset in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of coset in Pythagorean Numerology is: 8

Popularity rank by frequency of use

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Coset
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Coset
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=coset