The Projective Geometry of a Group
نویسنده
چکیده
We show that the pair (P(Ω),Gras(Ω)) given by the power set P = P(Ω) and by the “Grassmannian” Gras(Ω) of all subgroups of an arbitrary group Ω behaves very much like a projective space P(W ) and its dual projective space P(W ∗) of a vector space W . More precisely, we generalize several results from the case of the abelian group Ω = (W,+) (cf. [BeKi10a]) to the case of a general group Ω. Most notably, pairs of subgroups (a, b) of Ω parametrize torsor and semitorsor structures on P . The rôle of associative algebras and -pairs from [BeKi10a] is now taken by analogs of near-rings.
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