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| | GROUPS - Online Information article about GROUPS |
 | | In speaking of an operation, an object or a set of objects to which it may be applied is postulated; and the operation may, and generally will, have no meaning except in regard to such a set of objects. |
 | | The independent generating operations of a group may be subject to certain relations connecting them, but these must be such that it is impossible by combining them to obtain a relation expressing one operation in terms of the others. |
 | | The operation that results from carrying out additions, subtractions, multiplications and divisions, of and by integers a finite number of times, is represented by the relation x' =ax+b, where a and b are rational numbers of which a is not zero, x is the object of the operation, and x' is the result. |
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