Groups and Symmetry¶
Armstrong, M. A. (1988). Groups and Symmetry. Springer.
Cited by¶
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Primes¶
- Group
- The reason a group is a prime, and not merely a piece of mathematics, is that the same skeleton organizes the analysis of physical systems (gauge symmetries and conservation laws), cryptosystems (discrete logarithms and elliptic-curve points), moves on combinatorial objects (a Rubik's cube, a shuffled deck), music-theoretic transformations (transposition and inversion), and role permutations in social structures.
This sourceDevelops group theory explicitly as the mathematics of symmetry, with group actions, orbits, stabilisers, Lagrange's theorem, and the wallpaper groups.
- The reason a group is a prime, and not merely a piece of mathematics, is that the same skeleton organizes the analysis of physical systems (gauge symmetries and conservation laws), cryptosystems (discrete logarithms and elliptic-curve points), moves on combinatorial objects (a Rubik's cube, a shuffled deck), music-theoretic transformations (transposition and inversion), and role permutations in social structures.
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