Let K be a finite, connected, abstract simplicial complex. The Morse complex of K, first introduced by Chari and Joswig, is the constructed from all gradient vector fields on K. We show that if neither boundary n-simplex nor cycle, then Aut(M(K))≅Aut(K). In case where K=Cn, cycle length n, we Aut(M(Cn))≅Aut(C2n). When K=∂Δn, prove Aut(M(∂Δn))≅Aut(∂Δn)×Z2. These results are based recent work Cap...

We investigate the extent to which Slaman and Woodin’s framework for the analysis of the automorphism group of the structure of the Turing degrees can be transferred to analyze the automorphism group of the structure of the enumeration degrees.

We show that certain finite groups do not arise as the automorphism group of the square of a finite algebraic structure, nor as the automorphism group of a finite, 2-generated, free, algebraic structure.

Let Fn be a free group of rank n. An automorphism of Fn is called an IA-automorphism if it trivially acts on the abelianization H of Fn. We denote by IAn the group of IA-automorphisms and call it the IA-automorphism group of Fn. For any integer d ≥ 2, let IAn,d be the group of automorphisms of Fn which trivially acts on H⊗ZZ/dZ. We call IAn,d the congruence IA-automorphism group of Fn of level ...

We call a Clayey graph Γ = Cay(G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aunt(Γ). in this paper, we give a classification of all non-normal Clayey graphs of finite abelian group with valency 6. 

Denote the n × n toroidal queen’s graph by Qn. We find its automorphism group Aut(Qn) for each positive integer n, showing that for n ≥ 6, Aut(Qn) is generated by the translations, the group of the square, the homotheties, and (for odd n) the automorphism (x, y) → (y + x, y − x). For each n we find the automorphism classes of edges of Qn, in particular showing that for n > 1, Qn is edge-transit...