coset

suomi-englanti sanakirja

coset englanniksi

  1. 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.

  2. 1970 Wesley, Frederick W. Byron, Robert W. Fuller, ''Mathematics of Classical and Quantum Physics'', Volumes 1-2, Dover, 1992, page 597,

  3. 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.
  4. 1982 Thornes, Linda Bostock, Suzanne Chandler, C. Rourke, ''Further Pure Mathematics'', (w), 2002 Reprint, page 614,

  5. In general, the coset in row ''x'' consists of all the elements ''xh'' as ''h'' runs through the various elements of ''H''.
  6. {{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