✦ LIBER ✦

Realizing Finite Groups in Euclidean Space

✍ Scribed by Michael O Albertson; Debra L Boutin

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 97 KB
Volume: 225
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8189

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✦ Synopsis

A set of points W in Euclidean space is said to realize the finite group G if the isometry group of W is isomorphic to G. We show that every finite group G can be realized by a finite subset of some n , with n < G . The minimum dimension of a Euclidean space in which G can be realized is called its isometry dimension. We discuss the isometry dimension of small groups and offer a number of open questions.

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