'Abstract group' presentation slideshows

Binary Operations

Binary Operations. Let S be any given set. A binary operation ? on S is a correspondence that associates with each ordered pair (a, b) of elements of S a uniquely determined element a ? b = c where c ? S. Discussion. Can you determine some other binary operations on the whole numbers?

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Terminology :

On Representations of Abstract Groups as Automo r phism Groups of Graphs. Archil Kipiani Iv . Javakhishvili Tbilisi State University Winter School 2011 Hejnice This research was supported by Rustaveli NSF Grant-GNSF/ST 09_144_3-105. Terminology :.

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Cayley Theorem

Cayley Theorem. Every group is isomorphic to a permutation group. Example: U(10). U(10) = {1, 3, 7, 9} Definition: For g in U(10), let T g (x)= gx T 1 (x) = T 3 (x) = T 7 (x) = T 9 (x) =. x. T 1 =. ?. (1 3 9 7). 3x. T 3 =. (1 7 9 3). 7x. T 7 =. 9x. T 9 =.

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