Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

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


Relations in hyperreflection groups

Author: Erich W. Ellers
Journal: Proc. Amer. Math. Soc. 81 (1981), 167-171
MSC: Primary 20H15; Secondary 20F05, 20H20, 51F15
MathSciNet review: 593448
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Hyperreflection groups $ {G_m}$ are generalizations of groups generated by reflections. A hyperreflection group is generated by hyperreflections if $ \dim V$ is finite. A hyperreflection is a simple mapping $ \sigma $ such that $ \det \sigma = \gamma $, where $ {\gamma ^m} = 1$. If the field of scalars is commutative, the order of $ \sigma $ is $ m$. Our main result states that every relation between hyperreflections and their inverses is a consequence of relations of lengths 2, 4, and $ m$. The most interesting special case occurs for $ m = 2$. Then our result refers to relations between reflections.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20H15, 20F05, 20H20, 51F15

Retrieve articles in all journals with MSC: 20H15, 20F05, 20H20, 51F15

Additional Information

PII: S 0002-9939(1981)0593448-4
Article copyright: © Copyright 1981 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia