Group theory: Difference between revisions

Latest revision as of 15:56, 20 May 2008

Group theory is the area of mathematics which deals directly with the study of groups.

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 '''Group theory''' is the area of mathematics which deals directly with the study of [[group]]s.
-In order for a set <math>G</math> to be considered a group, it must have the following four properties:
+{{stub}}
-) An operation <math>*</math> (such as addition or multiplication, although multiplication is standard) is defined on <math>G</math>.
+== Topics and results in group theory ==
-)<math>G</math> has an has an identity element <math>j</math> under <math>*</math> such that for any element <math>a</math> in <math>G</math>, <math>j*a=a*j=a</math>.
-)The operation is associative, which means for any three elements <math>a</math>,  ''b'', and ''c'' in ''G'', (''a''*''b'')*''c''=a*(''b''*''c'')
-)Every element ''a'' in ''G'' has an inverse "x" under * that is also in ''G'' such that ''a''*''x''=''x''*''a''=''j''.
+* [[Coset]]s
-{{stub}}
+* [[Normal subgroup]]s
+* [[Lagrange's Theorem]]
+* [[Jordan-Hölder Theorem]]
+* [[Orbit]]
+* [[Stabilizer]]
+* [[Sylow Theorems]]
+* [[Free group]]s
+* [[Free abelian group]]s
 [[Category:Group theory]]