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.

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...

In this paper we find a necessary and sufficient condition for a finite nilpotent group to have an abelian central automorphism group.