Coset in Scrabble and Meaning

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Valid words made from Coset

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5-letter words (5 found)

4-letter words (12 found)

3-letter words (14 found)

2-letter words (8 found)

1-letter words (1 found)

You can make 40 words from coset according to the Scrabble US and Canada dictionary.

All 5 letters words made out of coset

coset ocset csoet scoet oscet socet coest ocest ceost ecost oecst eocst cseot sceot cesot ecsot secot escot osect soect oesct eosct seoct esoct coste ocste csote scote oscte socte cotse octse ctose tcose otcse tocse cstoe sctoe ctsoe tcsoe stcoe tscoe ostce sotce otsce tosce stoce tsoce coets ocets ceots ecots oects eocts cotes octes ctoes tcoes otces toces cetos ectos cteos tceos etcos tecos oetcs eotcs otecs toecs etocs teocs cseto sceto cesto ecsto secto escto csteo scteo ctseo tcseo stceo tsceo cetso ectso cteso tceso etcso tecso setco estco steco tseco etsco tesco osetc soetc oestc eostc seotc esotc ostec sotec otsec tosec stoec tsoec oetsc eotsc otesc toesc etosc teosc setoc estoc steoc tseoc etsoc tesoc

Note: these 'words' (valid or invalid) are all the permutations of the word coset. These words are obtained by scrambling the letters in coset.

Definitions and meaning of coset

coset

Etymology

co- +‎ set; apparently first used 1910 by American mathematician George Abram Miller.

Noun

coset (plural cosets)

1. (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.

Usage notes

Mathematically, given a group ${\displaystyle G}$ with binary operation ${\displaystyle \circ }$, element ${\displaystyle g\in G}$ and subgroup ${\displaystyle H\subseteq G}$, the set ${\displaystyle \left\{g\circ h:h\in H\right\}}$, which also defines the left coset if ${\displaystyle G}$ 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