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arXiv · 1201.6201

The projective geometry of a group

Wolfgang Bertram
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Abstract

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.

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Wolfgang Bertram. 2012-01-30. The projective geometry of a group. https://arxiv.org/abs/1201.6201

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