2012/01/30 by Wolfgang Bertram, Bertram, Wolfgang
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.1201.6201
openalex publication_date 2012/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the pair given by the power set and by the "Grassmannian"(set of all subgroups) of an arbitrary group behaves very much like the pair given by a projective space and its dual projective space. More precisely, we generalize several results from preceding joint work with M. Kinyon (arXiv:0903.5441), which concerned abelian groups, to the case of general non-abelian groups. Most notably, pairs of subgroups parametrize torsor and semitorsor structures on the power set. The rôle of associative algebras and -pairs from loc. cit. is now taken by analogs of near-rings.