2012/07/19 by Philippe Cara, Cara, Philippe, Sara Rottey +3
Engineering · Mathematics · #20D45 #51E20 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.CO #math.GR #msc:20D45 #msc:51E20
paper · pdf · doi:10.48550/arxiv.1207.4726
14 pages
openalex publication_date 2012/07/19 · arxiv created 2013/01/10 · arxiv updated 2013/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the isomorphism problem for linear representations. A linear representation Tn*(K) of a point set K is a point-line geometry, embedded in a projective space PG(n+1,q), where K is contained in a hyperplane. We put constraints on K which ensure that every automorphism of Tn*(K) is induced by a collineation of the ambient projective space. This allows us to show that, under certain conditions, two linear representations Tn*(K) and Tn*(K') are isomorphic if and only if the point sets K and K' are PGammaL-equivalent. We also deal with the slightly more general problem of isomorphic incidence graphs of linear representations. In the last part of this paper, we give an explicit description of the group of automorphisms of Tn*(K) that are induced by collineations of PG(n+1,q).