(algebra, group theory) The set that results from applying a group's binary operation with a given fixed element of the group on each element of a given subgroup.
Used in a Sentence
coset
Definition, parts of speech, synonyms, and sentence examples for coset.
Editorial note
It is not different than writing $r+I$ for a coset.
Examples3
Definitions1
Parts of speech1
Quick take
(algebra, group theory) The set that results from applying a group's binary operation with a given fixed element of the group on each element of a given subgroup.
Meaning at a glance
The clearest senses and uses of coset gathered in one view.
Definitions
Core meanings and parts of speech for coset.
noun
(algebra, group theory) The set that results from applying a group's binary operation with a given fixed element of the group on each element of a given subgroup.
Example sentences
It is not different than writing $r+I$ for a coset.
I feel its not that bad an abuse of notation as kinda consistent with other areas of mathematics - A coset, quotients r + I, affine subspaces v + W, etc.
In the second part we develop the equivariant fundamental group and use it to determine the topology of the space of loops with a given symmetry, which we show is related to certain cosets of the pure braid group in the full braid group, and to centralizers of elements of the corresponding coset.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use coset in a sentence?
It is not different than writing $r+I$ for a coset.
What does coset mean?
(algebra, group theory) The set that results from applying a group's binary operation with a given fixed element of the group on each element of a given subgroup.
What part of speech is coset?
coset is commonly used as noun.