coset
suomi-englanti sanakirjacoset englanniksi
The set that results from applying a group's operation with a given fixed element of the group on each element of a given subgroup.
1970 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 Thornes, Linda Bostock, Suzanne Chandler, C. Rourke, ''Further Pure Mathematics'', (w), 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''.
{{quote-book|en|year=2009|author=Lindsay N. Childs|title=A Concrete Introduction to Higher Algebra|edition=3rd|pageurl=https://books.google.com.au/books?id=qyDAKBr_I2YC&pg=PA231&dq=%22coset%22%7C%22cosets%22&hl=en&sa=X&ved=0ahUKEwjD9PCskfPaAhVJwZ8KHUIhAawQ6AEIQDAEv=onepage&q=%22coset%22%7C%22cosets%22&f=false|page=231|publisher=Springer