2020/02/10 by François Zara, Zara, François
Materials Science · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2002.03608
openalex publication_date 2020/02/10 · openalex created_date 2020/02/14 · openalex updated_date 2026/07/28
In this third part, we make the following hypothesis: representation R=R(α,β,γ;l) of W(p,q,r) is reducible and there exist a G-invariant non-nulle bilinear form where G=Im R. With those conditions, we know the structure of G: G'=G/N(G) is isomorphic to a finite dihedral group and N(G) is given explicitly as well as the action of G on N(G). We begin by giving conditions on p,q,r as well on α,β,γ and we proove them in the appendix. The general case will be studied in the next part.