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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Translations in certain groups of affine motions


Author: John Scheuneman
Journal: Proc. Amer. Math. Soc. 47 (1975), 223-228
MSC: Primary 22E25; Secondary 17B30
MathSciNet review: 0372120
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Abstract: The purpose of this article is to prove the conjecture of L. Auslander that every nilpotent group of affine motions of $ {{\mathbf{R}}^n}$ that is simply transitive on $ {{\mathbf{R}}^n}$ has a nontrivial translation in its center. The preliminary result that every such group is unipotent is of independent interest.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0372120-7
PII: S 0002-9939(1975)0372120-7
Keywords: Simply transitive nilpotent group of affine motions, unipotent, translation
Article copyright: © Copyright 1975 American Mathematical Society