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...

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.

An asymmetric coloring of a graph is its vertices that not preserved by any non-identity automorphism the graph. The motion minimal degree group, i.e., minimum number elements are moved (not fixed) automorphism. We confirm Tom Tucker's “Infinite Motion Conjecture” connected locally finite graphs with infinite admit an 2-coloring. infer this from more general result inverse limit sequence permut...

Up to isomorphism there are four symmetric (36,15,6) designs with automorphisms of order 7. Full automorphism group of one of them is the Chevalley group G(2, 2) ~ U(3,3) : Z2 of order 12096. Unitary group U(3,3) acts transitively on that design.

It has been shown that if a (v,k,λ )-symmetric design with λ ≤ 3 admits a flag-transitive automorphism group G which acts primitively on points, then G must be of affine or almost simple type. Here we extend the result to λ = 4.

We develop a theory of generalized presentations of groups. We give generalized presentations of the symmetric group Σ(X) and of the automorphism group of the free group of countable rank, Aut(Fω).

A k–factorization of Kv of type (r, s) consists of k–factors each of which is the disjoint union of r copies of Kk+1 and s copies of Kk,k. By means of what we call the patterned k–factorization Fk(D) over an arbitrary group D of order 2s + 1, it is shown that a k-factorization of type (1, s) exists for any k > 2 and for any s > 1 with D being an automorphism group acting sharply transitively on...

We describe symmetric designs D with classical parameters v=(q 6 − 1)/(q − 1), k=(q 5 − 1)/(q − 1), l=(q 4 − 1)/(q − 1), and automorphism group Aut(G 2 (q)).

The existence of triplewhist tournaments for v players has recently been solved for all values of v except v = 17. For v = 12 and v = 13 a complete enumeration has shown the nonexistence of TWh (v), while constructions of TWh (v) have been presented for v > 17. For several values of v existence has been shown by constructing a TWh (v) with a prescribed, usually cyclic, automorphism group. In th...