International Standard Music Number 3 left to right. These weighted digits are added together. The check digit is the integer between 0 and 9 that makes the sum a multiple of 10. For instance, for the item with ISMN beginning 979-0-060-11561: As 85 mod 10 = 5, the check digit is 10 - 5 = 5 and the full number is 979-0-060-11561-5. For another example, Robert Fripp's collection of Guitar Craft scores has the ISMN 979-0-9016791-7-7. Given first 12 digits 979-0-9016791-7, the ISMN algorithm evaluates which implies that the check digit is indeed 7 (because 123+7=130=13x10). International Standard Music Number The International Standard Music
Opposite group it is equal to its opposite group. Also, every group formula_1 (not necessarily abelian) is naturally isomorphic to its opposite group: An isomorphism formula_10 is given by formula_11. More generally, any antiautomorphism formula_12 gives rise to a corresponding isomorphism formula_13 via formula_14, since Let formula_16 be an object in some category, and formula_17 be a right action. Then formula_18 is a left action defined by formula_19, or formula_20. Opposite group In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special