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Unformatted text preview: Homework 1 Solutions 1. There are six symmetries of an equilateral triangle: the identity, rotate clockwise by 120 rotate counterclockwise by 120 , and three mirror symmetries about lines which pass through one vertex and the opposite edge. In class we created a partial multiplication table for these symmetries. Complete this table. Solution: Define 1 to be the identity transform, to be rotation by 120 (so 2 is rotation by 240 . Let 1 be the reflection through the vertical line (through the center), 2 to be the reflection through the line at 30 , and 3 to be reflection through the line at 30 . Then depending on the interpretation of order, our Cayley table is one of the following: 1 2 1 2 3 1 1 2 1 2 3 2 1 3 1 2 2 2 1 2 3 1 1 1 2 3 1 2 2 2 3 1 2 1 3 3 1 2 2 1 1 2 1 2 3 1 1 2 1 2 3 2 1 2 3 1 2 2 1 3 1 2 1 1 3 2 1 2 2 2 1 3 1 2 3 3 2 1 2 1 2. Construct a group G with  G  = 3 (so G has exactly three elements)....
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This note was uploaded on 01/30/2012 for the course MATH 310 303 taught by Professor Rwk during the Spring '11 term at Simon Fraser.
 Spring '11
 RWK

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