# History of MathematicalGrouP

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 Revision 29 . . February 17, 2001 8:32 am by OpRgAg [Quoting future group related pages] Revision 28 . . (edit) February 17, 2001 8:03 am by UralicLanguages Revision 27 . . (edit) February 17, 2001 7:30 am by cobrand.bomis.com Revision 26 . . February 5, 2001 9:42 pm by RoseParks Revision 25 . . February 5, 2001 10:11 am by RoseParks Revision 24 . . (edit) January 29, 2001 6:39 am by JoshuaGrosse

Difference (from prior major revision) (author diff)

Changed: 28c28
 +Signed integers
 *Signed integers

Changed: 44c44
 +Group of geometric transformations of the plane.
 *Group of geometric transformations of the plane.

Changed: 55c55
 One can build more generally the group of all distance-preserving transformations of a space or set of points. In this case, the proof of the group axioms is bit more complicated and interesting. (OpRgAg).
 One can build more generally the group of all distance-preserving transformations of a space or of a set of points in a space. In this case, the proof of the group axioms is a bit more interesting. (OprgaG).

Removed: 58d57

Removed: 90d88

Changed: 92c90,92
 a and b are integers, but b is not = to 0, and the operation multiplication, denoted by "x," is (Q,x) a GrouP?
 a and b are integers, but b is not = to 0, and the operation multiplication, denoted by "x," is (Q,x) a GrouP?

Changed: 94c94
 Groups are important, too, because they are a fundamental algebraic structure. We can investigate groups with added properties like CommutativeGroups? and NonCommutativeGroups?, and also build other structures based on the notion of a group, but with more than one operations and more properties. This brings us to RinGs and FielDs.
 Groups are important as a fundamental algebraic structure and as a basic tool for embedding the mathematical properties of objects, even properties of groups themselves because one can built groups out of existing ones (see GroupProductS?, NoetherIsomorphismTheoremS?, WreathProduct?, BrauerGroup?, DerivedGroup?, GroupCenter?, GroupCharacter?, FittingSubgroup?, CohomologyGroups?). We can investigate groups with global properties like CommutativeGroups? and NonCommutativeGroups?, SimpleGroups? and SolvableGroups?, FinitelyGeneratedGroups?, AlgebraicGroups?, study how groups can be related via MorphisMs and also build other structures based on the notion of a group, but with more than one operation and/or more properties. This brings us to RinGs, FielDs, ModulEs.

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