'Permutation group' presentation slideshows

Algebraic Structures: Group Theory

Algebraic Structures: Group Theory. Today we are going to study the abstract properties of binary operations Groups Subgroups Rings Fields. Rotating a Square in Space. Imagine we can pick up the square, rotate it in any way we want, and then put it back on the white frame. F. F.

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presented by Anastasia Braginsky March 2012

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Algebraic Structures: Group Theory II

Algebraic Structures: Group Theory II. Group. A group G is a pair (S, ?), where S is a set and ? is a binary operation on S such that:. 1. ? is associative. 2. (Identity) There exists an element e ? S such that:. e ? a = a ? e = a, for all a ? S.

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Lecture-2 ????

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Q.1 Let 6 be an element of the permutation group S 5 . Then the maximum possible order of 6 is

Q.1 Let 6 be an element of the permutation group S 5 . Then the maximum possible order of 6 is. A] 5 B] 6 C] 10 D] 15 Ans B. Q.2 The number of group homomorphism's from the cyclic group Z 4 to the cyclic Z 7 is :. A] 7 B] 3 C] 2 D] 1 Ans is d.

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Theorem 6.6: Let [G; ? ] be a group and let a and b be elements of G. Then

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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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Permutation

Permutation. God Alone.com Advocating the worship of God Alone. What are Permutations?. Permutation is the rearranging in a orderly fashion objects or values. Mathematically it defines an operation which arranges a number of objects i.e. digits in a specific order. For Example.

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