Suppose that a group G acts transitively on the points of a nonDesarguesian plane, P. We prove first that the Sylow 2-subgroups of G are cyclic or generalized quaternion. We also prove that P must admit an odd order automorphism group which acts transitively on the set of points of P. 1 MSC(2000): 20B25, 51A35.

Based on Donaldson’s method, we prove that, for an integral Kähler class, when there is a Kähler metric of constant scalar curvature, then it minimizes the K-energy. We do not assume that the automorphism group is discrete.

If (W, S) is a right-angled Coxeter group, then Aut(W ) is a semidirect product of the group Aut◦(W ) of symmetric automorphisms by the automorphism group of a certain groupoid. We show that, under mild conditions, Aut◦(W ) is a semidirect product of Inn(W ) by the quotient Out◦(W ) = Aut◦(W )/Inn(W ). We also give sufficient conditions for the compatibility of the two semidirect products. When...

We present a class of transitive BLT-sets that contains several known examples and at least one new example over the field with 41 elements with automorphism group Z21 : (Z2 × Z2). This example is sporadic in the sense that it does not fall into any of the known infinite families of BLT-sets.

It is proved that the automorphism group of a semigroup being an inflation of its proper subsemigroup decomposes into a semidirect product of two groups one of which is a direct sum of full symmetric groups.

We give a general construction of coded systems with an automorphism group isomorphic to Z⊕G where G is any preassigned group which has a “continuous block presentation” (the isomorphism will map the shift to (1, eG)). Several applications are given. In particular, we obtain automorphism groups of coded systems which are abelian, which are finitely generated and one which contains Z[1/2]. We sh...

We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D = (K/F, σ, c), employing a K-automorphism τ and an element d ∈ D. These algebras appear in the construction of iterated spacetime block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly lo...

The main aim of this article is to study (v, k, λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3, q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2, q) and G ⩾ PSL(3, q).

We study a new construction of an invariant metric for compact subgroups of the automorphism group of a domain in complex space. Applications are provided.