different between coset vs colet
coset
English
Etymology
co- +? set; apparently first used 1910 by American mathematician George Abram Miller.
Noun
coset (plural cosets)
- (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.
- 1970 [Addison Wesley], Frederick W. Byron, Robert W. Fuller, Mathematics of Classical and Quantum Physics, Volumes 1-2, Dover, 1992, page 597,
- Theorem 10.5. The collection consisting of an invariant subgroup H and all its distinct cosets is itself a group, called the factor group of G, usually denoted by G/H. (Remember that the left and right cosets of an invariant subgroup are identical.) Multiplication of two cosets aH and bH is defined as the set of all distinct products z = xy, with x ? aH and y ? bH; the identity element of the factor group is the subgroup H itself.
- 1982 [Stanley Thornes], Linda Bostock, Suzanne Chandler, C. Rourke, Further Pure Mathematics, Nelson Thornes, 2002 Reprint, page 614,
- In general, the coset in row x consists of all the elements xh as h runs through the various elements of H.
- 2009, Lindsay N. Childs, A Concrete Introduction to Higher Algebra, Springer, 3rd Edition, page 231,
- Example 3. Let (the operation is ), . Then the coset is the set of integers of the form where runs through all elements of .
- 1970 [Addison Wesley], Frederick W. Byron, Robert W. Fuller, Mathematics of Classical and Quantum Physics, Volumes 1-2, Dover, 1992, page 597,
Usage notes
Mathematically, given a group with binary operation , element and subgroup , the set , which also defines the left coset if is not assumed to be abelian.
The concept is relevant to the (mathematical) definitions of normal subgroup and quotient group.
Derived terms
- double coset
- left coset
- right coset
Translations
Further reading
- Lagrange's theorem (group theory) on Wikipedia.Wikipedia
- Normal subgroup on Wikipedia.Wikipedia
- Quotient group on Wikipedia.Wikipedia
- Coset on Wolfram MathWorld
- Coset in a group on Encyclopedia of Mathematics
Anagrams
- Coste, Cotes, OTECs, ScotE, cotes, scote
coset From the web:
- what cosetta mean
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colet
English
Alternative forms
- collet
Etymology
From acolyte.
Noun
colet (plural colets)
- (obsolete) A lower servant in a church.
Anagrams
- Celto-, clote, telco
Latin
Verb
c?let
- third-person singular present active subjunctive of c?l?
Romanian
Etymology
From French colis
Noun
colet n (plural colete)
- parcel
Declension
colet From the web:
- what colette stores are closing
- colette meaning
- what colors make brown
- what colors make red
- what colors make black
- what colors make yellow
- what's coleto mean in spanish
- what's coleta in english
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