Difference between revisions of "Group theory"
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'''Group theory''' is the area of mathematics which deals directly with the study of [[group]]s. | '''Group theory''' is the area of mathematics which deals directly with the study of [[group]]s. | ||
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| + | In order for a set ''G'' to be considered a group, it must have the following four properties: | ||
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| + | 1) An operation * (such as addition or multiplication, although multiplication is standard) is defined on ''G''. | ||
| + | 2)G has an has an identity element ''j'' under * such that for any element ''a'' in ''G'', ''j''*''a''=''a''*''j''=''a''. | ||
| + | 3)The operation is associative, which means for any three elements ''a'', ''b'', and ''c'' in ''G'', (''a''*''b'')*''c''=a*(''b''*''c'') | ||
| + | 4)Every element ''a'' in ''G'' has an inverse "x" under * that is also in ''G'' such that ''a''*''x''=''x''*''a''=''j''. | ||
Revision as of 19:06, 13 March 2008
Group theory is the area of mathematics which deals directly with the study of groups.
In order for a set G to be considered a group, it must have the following four properties:
1) An operation * (such as addition or multiplication, although multiplication is standard) is defined on G. 2)G has an has an identity element j under * such that for any element a in G, j*a=a*j=a. 3)The operation is associative, which means for any three elements a, b, and c in G, (a*b)*c=a*(b*c) 4)Every element a in G has an inverse "x" under * that is also in G such that a*x=x*a=j.
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