## On the automorphism group of some pro-ℓ fundamental groups

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 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 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 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 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 Order

In this paper we are interested in the automorphism group of the poset Bm, n. Bm, n constitutes the words obtained from the cyclic word of length n on an alphabet of m letters in by deleting on all possible ways and their natural order. We prove: Résumé: Le but de ce papier est la détermination du groupe d"automorphismes des ordres Bm, n. Il s"agit...

Published in Order

This paper deals with the automorphism group of the partial order of finite traces. We show that any group can arise as such an automorphism group if we allow arbitrary large dependence alphabets. Restricting to finite dependence alphabets, the automorphism groups are profinite and possess only finitely many simple decomposition factors. Finally, w...

Published in Designs, Codes and Cryptography

Affine-invariant codes are extended cyclic codes of length pm invariant under the affine-group acting on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\text{F}}_{p^...

Published in Designs, Codes and Cryptography

We show that the automorphism group of a divisible design \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${\mathcal{D}}$$ \end{document} is isomorphic to a subgroup H ...