The polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism, that is, a nontrivial automorphism whose cycles all have the same length. In this paper we investigate the existence of semiregular automorphisms of edge-transitive graphs. In particular, we show that any regular edge-transitive graph of valency three or four has a semiregular automorphism.

We determine the quantum automorphism groups of finite graphs. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group D4.

The present paper investigates the groups of automorphisms for some lattices of modal logics. The main results are the following. The lattice of normal extensions of S4.3, NExtS4.3, has exactly two automorphisms, NExtK.alt1 has continuously many automorphisms. Moreover, any automorphism of NExtS4 fixes all logics of finite codimension. We also obtain the following characterization of pretabular...

The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and analogous results for finite groups. The second part considers hypersurfaces of finite Catlin multitype, and the Kohn-Nirenberg phenomenon in higher dimensions...

We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the constants are not “closed” in suitable senses. We also improve the definitions and results from [15] on generalized strongly normal extensions, using this to...

We construct a new ovoid of the polar space arising from the Hermitian surface of PGð3; qÞ with qd 5 odd. The automorphism group G of such an ovoid has a normal cyclic subgroup F of order 12 ðqþ 1Þ such that G=FGPGLð2; qÞ. Furthermore, G has three orbits on the ovoid, one of size qþ 1 and two of size 12 qðq 1Þðqþ 1Þ.

Let G be a profinite group and let α be an automorphism of G. Then α is topologically intense if, for every closed subgroup H of G, there exists x ∈ G such that α(H) = xHx. Topologically intense automorphisms are automatically continuous, because they stabilize each open normal subgroup of the group on which they are defined. We denote by Intc(G) the group of topologically intense automorphisms...

In this paper, we describe all automorphism-liftable torsion modules over non-primitive hereditary Noetherian prime rings. We also study non-torsion not necessarily commutative Dedekind

Abstract In this paper, we are interested in the asymptotic enumeration of Cayley graphs. It has previously been shown that almost every digraph smallest possible automorphism group: is, it is a digraphical regular representation (DRR). approach corresponding question for undirected The situation complicated by fact there two infinite families groups do not admit any graphical (GRR). strategy d...

Let F be a perfect field and M(F ) the nonassociative simple Moufang loop consisting of the units in the (unique) split octonion algebra O(F ) modulo the center. Then Aut(M(F )) is equal to G2(F )o Aut(F ). In particular, every automorphism of M(F ) is induced by a semilinear automorphism of O(F ). The proof combines results and methods from geometrical loop theory, groups of Lie type and compo...