Automata groups generated by Cayley machines of groups of nilpotency class two

A Fractal Non-Contracting Class of Automata Groups

A Class of Two Generated Automaton Groups on a Three Letter Alphabet

Cayley graphs of finitely generated groups

There does not exist a Borel choice of generators for each finitely generated group which has the property that isomorphic groups are assigned isomorphic Cayley graphs.

On the nilpotency class of the automorphism group of some finite p-groups

Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the Frattini subgroup of $G$. It is shown that the nilpotency class of $Autf(G)$, the group of all automorphisms of $G$ centralizing $G/ Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of maximal class. We also determine the nilpotency class of $Autf(G)$ when $G$ is a finite abelian $p$-group.

Automorphism groups of Cayley graphs generated by connected transposition sets

Let S be a set of transpositions that generates the symmetric group Sn, where n ≥ 3. The transposition graph T (S) is defined to be the graph with vertex set {1, . . . , n} and with vertices i and j being adjacent in T (S) whenever (i, j) ∈ S. We prove that if the girth of the transposition graph T (S) is at least 5, then the automorphism group of the Cayley graph Cay(Sn, S) is the semidirect p...