In a group trellis, the sequence of branches that split from the identity path and merge to the identity path form two normal chains. The Schreier refinement theorem can be applied to these two normal chains to obtain a Schreier series, a normal chain of the branch group B of the group trellis. It is shown that the components of the shortest length generator sequences of Forney and Trott form a...

We call a Cayley digraph X = Cay(G, 8) normal for G if the right regular representation R( G) of G is normal in the full automorphism group Aut(X) of X. In this paper we determine the normality of Cayley digraphs of groups of order twice a prime.

A Cayley graph Γ = Cay(G,S) is said to be normal for a finite group G, if the right regular representation R(G) is normal in the full automorphism group Aut(Γ) of Γ. In this paper we investigate the normality of Cayley graphs of groups of order a product of two distinct primes, by determining all nonnormal Cayley graphs of these groups.

We show that for every “locally finite” unit-preserving completely positive map P acting on a C∗-algebra, there is a corresponding ∗-automorphism α of another unital C∗-algebra such that the two sequences P, P , P , . . . and α,α, α, . . . have the same asymptotic behavior. The automorphism α is uniquely determined by P up to conjugacy. Similar results hold for normal completely positive maps o...

Abstract. The normal symmetric triality algebras (STA’s) and the normal Lie related triple algebras (LRTA’s) have been recently introduced by the second author, in connection with the principle of triality. It turns out that the unital normal LRTA’s are precisely the structurable algebras extensively studied by Allison. It will be shown that the normal STA’s (respectively LRTA’s) are the algebr...

A Cayley graph Γ = Cay(G, S) is called normal for G, if GR, the right regular representation of G, is a normal subgroup of the full automorphism group Aut(Γ ) of Γ . In this paper we determine the normality of connected and undirected Cayley graphs of valency three for dihedral groups. 2000 Mathematics Subject Classification: 05C25, 20B25.

Abstract We show that any normal irreducible affine n -dimensional SL -variety X is determined by its automorphism group seen as an ind-group in the category of varieties. In other words, if Y algebraic variety such Aut( ) ≃ ind-group, then a variety. If we drop condition normality on , this statement fails. case ≥ 3, result above holds true replace

A Cayley graph Cay(G,S) on a group G is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of Cay(G,S). In this paper, all connected tetravalent non-normal Cayley graphs of order 4p are constructed explicitly for each prime p. As a result, there are fifteen sporadic and eleven infinite families of tetravalent non-normal Cayley graphs of orde...