The projective geometry of a group
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 obtained in joint work with
M. Kinyon
for abelian groups (cf. preprint 271 on this server) to the case of a
general group.
Most notably, pairs of subgroups (a,b) 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.
(Remark on terminology : we have changed the term "groud", used in the above
mentioned paper, to the more commonly used and more fashionable "torsor".)
Wolfgang Bertram < bertram@iecn.u-nancy.fr >