Published in Order
We show that there are just countably many countable homogeneous semilattices and give an explicit description of them. For the countable universal homogeneous semilattice we show that its automorphism group has a largest proper nontrivial normal subgroup.
Published in Designs, Codes and Cryptography
Let K(n,r) denote the minimum cardinality of a binary covering code of length n and covering radius r. Constructions of covering codes give upper bounds on K(n,r). It is here shown how computer searches for covering codes can be sped up by requiring that the code has a given (not necessarily full) automorphism group. Tabu search is used to find orb...
Published in Mathematical Notes
In the paper it is proved that the projective groupL2(q) cannot be the automorphism group of a finite left distributive quasigroup. This is a special case of the conjecture according to which the automorphism group of a left distributive quasigroup is solvable.
Published in Geometriae Dedicata
In this paper we study a natural generalization of Platonic solids: two-dimensional simply connected polygonal complexes with flag transitive group of combinatorial automorphisms. Our results give an almost complete description of such symmetric complexes with constant valency 3. The initial local data for the construction of such a complex are a r...
Published in Chinese Science Bulletin
An edgee of a graphG is called a fixed edge if G −e +e′ ≅ G impliese′ = e, and an isomorphic fixed edge if G −e + e′ ≅ G implies that there exists an automorphism of G −e, which maps the ends ofe to the ends ofe′. It is proved that almost every graph is with all its edges as fixed edges and isomorphic fixed edges, and it is conjectured that all gra...
Published in The Journal of Geometric Analysis
Let P be a bounded analytic polyhedron in ℂ2 whose boundary is smooth except for normal crossing singularities. We show that P is a holomorphic quotient of the bidisc, if its automorphism group is noncompact.
Published in Korean Journal of Computational & Applied Mathematics
LetG denote either of the groupsGL2(q) orSL2(q). The mapping θ sending a matrix to its transpose-inverse is an automophism ofG and therefore we can form the groupG+ =G. . In this paper conjugacy classes of elements inG+ -G are found. These classes are closely related to the congruence classes of invertible matrices inG.
Published in Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
We take a further step toward the classification of all flat (2-dimensional) Laguerre planes of group dimension 4 by determining, up to isomorphism, all such Laguerre planes that admit 4-dimensional groups of automorphisms that fix at least two parallel classes. It is shown that these planes occur among those flat Laguerre planes of generalised she...
