Three Examples of Groups Associated with Repetitive Patterns
Consider the cyclic pattern below. It suggests the finite group C6 consisting of six rotations clockwise of 0°, 60°, 120°, …: any of these applied to the pattern leaves it invariant. The set of transformations might be named 1, T, T2, T3, T4, T5 or in a slightly different form T−2, T−1, 1, T, T2, T3: then T stands for a clockwise rotation of 60°, T3 for the sanie rotation repeated three times and T−1 for the inverse rotation of 60° anti-clockwise.
KeywordsNormal Subgroup Finite Group Initial Arrangement Congruence Class Repetitive Pattern
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