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abelian abelian group affine algebra analytic ascending chain condition assume bounded co-ordinates collineation groups column condition conic conies conjugate consider construction contains contradiction converges convex Corollary corresponding cosets countable cyclic d-polytope d'ordre defined definition denote direct sum distinct edges élément elements equation equivalent exists finite number following theorem function given graph Hence implies induction infinite integer intersect irreducible isomorphic isotopy l)-faces lattice packing Lemma Let G linear M+(K Math matrix Mellin transform minimal modular maximal Moore space Moulton planes nilpotent nodal non-degenerate non-zero normal subgroup obtain open set pair of lines parabola paracompact permutation polynomial polytope positive integer prime projective plane proof of Theorem Proposition prove representation result right ideal ring satisfies sequence Souslin spheres subgroup subset Suppose Sylow tangent Theorem topological topological ring trace transform transitive unique vector vertex vertices zero