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| | group. The Columbia Encyclopedia, Sixth Edition. 2001-05 |
 | | 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. |
| www.bartleby.com /65/gr/group.html (205 words) |
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