‎motivated by a celebrated theorem of schur‎, ‎we show that if~$gamma$ is a normal subgroup of the full automorphism group $aut(g)$ of a group $g$ such that $inn(g)$ is contained in $gamma$ and $aut(g)/gamma$ has no uncountable abelian subgroups of prime exponent‎, ‎then $[g,gamma]$ is finite‎, ‎provided that the subgroup consisting of all elements of $g$ fixed by $gamma$ has finite index‎. ‎so...

The modified bubble-sort graph of dimension n is the Cayley graph of Sn generated by n cyclically adjacent transpositions. In the present paper, it is shown that the automorphism group of the modified bubble sort graph of dimension n is Sn×D2n, for all n ≥ 5. Thus, a complete structural description of the automorphism group of the modified bubble-sort graph is obtained. A similar direct product...

We characterize the automorphism groups of circulant digraphs whose connection sets are relatively small, and of unit circulant digraphs. For each class, we either explicitly determine the automorphism group or we show that the graph is a “normal” circulant, so the automorphism group is contained in the normalizer of a cycle. Then we use these characterizations to prove results on the automorph...

In this paper we develop a theory of translation groups for dimensional dual hyperovals and APN functions. It will be seen that both theories can be treated, to a large degree, simultaneously. For small ambient spaces it will be shown that the translation groups are normal in the automorphism group of the respective geometric object. For large ambient spaces there may be more than one translati...

In this paper it is proved that having a logarithm is e1uivalent to having roots of arbitrary order in the group of automorphisms of a formal power series ring, and in algebraic subgroups, too. INTRODUCTION The question whether an automorphism of a complex formal power series ring has an iteration, or may be embedded in a one parameter group has received much attention lately. The original sett...

Let p be a prime,G a finite group which has a normal p-subgroup containing its own centralizer inG, and R a commutative local ring with residue class field of characteristic p. In this paper, it is shown that if α is an augmented automorphism of RG which fixes a Sylow p-subgroup P of G, there is ρ ∈ Aut(G) such that xαρ = x for all x ∈ P , and αρ is an inner automorphism of RG.

The modified bubble-sort graph of dimension n is the Cayley graph of Sn generated by n cyclically adjacent transpositions. In the present paper, it is shown that the automorphism group of the modified bubble sort graph of dimension n is Sn × D2n, for all n ≥ 5. Thus, a complete structural description of the automorphism group of the modified bubble-sort graph is obtained. A similar direct produ...

Letting τ denote the inverse transpose automorphism of GL(n, q), a formula is obtained for the number of g in GL(n, q) so that gg is equal to a given element h. This generalizes a result of Gow and Macdonald for the special case that h is the identity. We conclude that for g random, gg behaves like a hybrid of symplectic and orthogonal groups. It is shown that our formula works well with both c...

In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...