The Isometry Dimension and Orbit Number of a Finite Group
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چکیده
A finite set W ⊂ R is said to realize the group G if the isometry group of W is isomorphic to G. The isometry dimension of a group is the minimum dimension of a realization. It is known that the isometry dimension of G is less than |G| [1]. We show that the isometry dimension of Z2 is n. The orbit number of a group is the minimum number of orbits in a realization. We show that the groups Z2 are the only abelian groups with orbit number 1. We provide examples that illuminate these parameters.
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تاریخ انتشار 2001