| 1. | As another example consider the group of symmetries of a square.
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| 2. | The dihedral group D 12 is the group of symmetries of a hexagon.
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| 3. | The Lorentz group is a Lie group of symmetries of the spacetime of special relativity.
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| 4. | A string written in boldface represents a group of symmetries of Euclidean 3-space.
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| 5. | Similar equations can be written for any one-parameter unitary group of symmetries of the physical system.
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| 6. | The functional measure would have to be invariant under the one parameter group of symmetry transformation as well.
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| 7. | The same function may be an invariant for one group of symmetries and equivariant for a different group of symmetries.
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| 8. | The same function may be an invariant for one group of symmetries and equivariant for a different group of symmetries.
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| 9. | The related einstein problem asks for a shape that can tile space but not with an infinite cyclic group of symmetries.
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| 10. | The effect proportional to the square of the electric field can exist only in crystals belonging to acentric point groups of symmetry.
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