Abstract
For a reflection space (P, Γ) [introduced in Karzel and Taherian (Results Math 59:213–218, 2011)] we define the notion “Reducible Subspace”, consider two subsets of \({\Gamma, \Gamma^{+} := \{a b\,|\, a,b \in P\}}\) and \({\Gamma^{-} := \{a b c\,|\, a, b, c \in P\}}\) and the map
We show, for each subspace S of (P, Γ), V := κ(S) is a v-subgroup (i.e. V is a subgroup of Γ+ with if \({\xi = xy \in V, \xi \neq 1}\) then \({x \cdot \overline{x,y}\subseteq V}\)) if and only if S is reducible. Our main results are stated in the items 1–5 in the introduction.
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Dedicated to Momme Johs Thomsen to mark his 70th birthday
S.-Gh. Taherian was partially supported by Diercks-von-Zweck-Stiftung in summer 2011.
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Karzel, H., Taherian, SG. Reflection Spaces and Corresponding Kinematic Structures. Results. Math. 63, 597–610 (2013). https://doi.org/10.1007/s00025-011-0220-z
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DOI: https://doi.org/10.1007/s00025-011-0220-z