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Less overwhelming, but still of interest, are some of the smaller General Linear Group s over Finite Fields . The group theorist J. L. Alperin has written that "The typical example of a finite group is GL(n,q), the general linear group of n dimensions over the field with q elements. The student who is introduced to the subject with other examples is being completely misled." (Bulletin (New Series) of the American Mathematical Society, 10 (1984) 121) For a discussion of one of the smallest such groups, GL(2,3), see [http://www.log24.com/theory/VisualizingGL2p.html Visualizing GL(2,p)]. Finite groups are directly relevant to Symmetry , when that is restricted to a finite number of transformations. It turns out that '' Continuous Symmetry '', as modelled by Lie Group s, also leads to finite groups, the Weyl Group s. In this way, finite groups and their properties can enter centrally in questions, for example in Theoretical Physics , where their role is not initially obvious. Every finite group of a Prime Order is Cyclic . NUMBER OF GROUPS FOR A GIVEN SET For each group type (group up to Isomorphism ) the number of groups for a given underlying set of ''n'' elements is ''n''! divided by the order of the Automorphism Group . SEE ALSO
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