Relations in hyperreflection groups
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- by Erich W. Ellers PDF
- Proc. Amer. Math. Soc. 81 (1981), 167-171 Request permission
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
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 167-171
- MSC: Primary 20H15; Secondary 20F05, 20H20, 51F15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0593448-4
- MathSciNet review: 593448