
 AllRefer.com  group (Mathematics)  Encyclopedia 
  The real numbers (see number) form a commutative group both under addition, with 0 as identity element and a as inverse, and, excluding 0, under multiplication, with 1 as identity element and 1/a as inverse. 
  The elements of a group need not be numbers; they may often be transformations, or mappings, of one set of objects into another. 
  Group theory has wide applications in mathematics, including number theory, geometry, and statistics, and is also important in other branches of science, e.g., elementary particle theory and crystallography. 
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