The $$\mathrm {L}_3(4)$$ L 3 ( 4 ) near octagon

The Valuations of the Near Octagon I4

The maximal and next-to-maximal subspaces of a nonsingular parabolic quadric Q(2n, 2), n ≥ 2, which are not contained in a given hyperbolic quadric Q+(2n − 1, 2) ⊂ Q(2n, 2) define a sub near polygon In of the dual polar space DQ(2n, 2). It is known that every valuation of DQ(2n, 2) induces a valuation of In. In this paper, we classify all valuations of the near octagon I4 and show that they are...

The valuations of the near octagon G4

On the Hall-Janko graph with 100 vertices and the near-octagon of order (2, 4)

In this paper, we construct the Hall-Janko graph within the split Cayley hexagon H(4). Using this graph we then construct the near-octagon of order (2, 4) as a subgeometry of the dual of H(4), with J2 : 2 as its automorphism group. These constructions are based on a lemma determining the possibilities for the structure of the intersection of two subhexagons of order 2 in H(4).

Modal $\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{u}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\tilde{\mathrm{l}}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{C}$ Logics and Predicate Superintuitionistic Logics: $\mathrm{C}_{0\Gamma \mathrm{r}\mathrm{e}..\mathrm{S}},\mathrm{p}$

In this note we deal with intuitionistic modal logics over $\mathcal{M}\mathcal{I}PC$ and predicate superintuitionistic logics. We study the correspondence between the lattice of all (normal) extensions of MTPC and the lattice of all predicate superintuitionistic logics. Let $\mathrm{L}_{Prop}$ denote a propositional language which contains two modal operators $\square$ and $\mathrm{O}$ , and $...

A New Near Octagon and the Suzuki Tower

We construct and study a new near octagon of order (2, 10) which has its full automorphism group isomorphic to the group G2(4) : 2 and which contains 416 copies of the Hall-Janko near octagon as full subgeometries. Using this near octagon and its substructures we give geometric constructions of the G2(4)-graph and the Suzuki graph, both of which are strongly regular graphs contained in the Suzu...