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Unformatted text preview: 1 / the inverse of .a;b/ . You are asked to check this in Exercise 3.1.1 . Denition 3.1.1. A B , with this group structure, is called the direct product of A and B . Example 3.1.2. Suppose we have two sets of objects, of different types, say ve apples on one table and four bananas on another table. Let A denote the group of permutations of the apples, A S 5 , and let B denote the group of permutations of the bananas, B S 4 . The symmetries of the entire conguration of fruit consist of permutations of the apples among themselves and of the bananas among themselves. That is, a symmetry is a pair of permutations .;/ , where 2 A and 2 B . Two such symmetries are composed by separately composing the symmetries of apples and the 147...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08