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.

The concept of graph symmetry is explained in terms of the vertex automorphism group, which is a subgroup of the complete vertex permutation group. The automorphism group can be deduced from the automorphism partition of graph vertices. An algorithm is described which constructs the automorphism group of a graph from the automorphism vertex partitioning. The algorithm is useful especially for g...

Scmicomplctc nilpotcnt groups, that is, nilpotent groups with no outer automorphisms, have been of interest for many years. In this paper pscudocomplete nilpotent groups, that is, nilpotent groups in which the automorphism group and the inner automorphism group arc isomorphic (not equal), are constructed. When suitable conditions are placed on the pseudocomplete nilpotent group, the quotient of...

We show that the TeichmuK ller space of the triangle groups of type (p, q,R) in the automorphism group of the two-dimensional complex hyperbolic space contains open sets of 0, 1 and two real dimensions. In particular, we identify the TeichmuK ller space near embeddings of the modular group preserving a complex geodesic. 2002 Elsevier Science Ltd. All rights reserved. MSC: 32H20; 20H10; 22E40; 5...

We prove that the conformal automorphism group of a countably connected circular region of connectivity at least three is either a Fuchsian group or a discrete elementary group of Möbius transformations.

In this paper we consider the Suzuki curve y + y = x0(x + x) over the field with q = 2 elements. The automorphism group of this curve is known to be the Suzuki group Sz(q) with q(q − 1)(q + 1) elements. We construct AG codes over Fq4 from a Sz(q)-invariant divisor D, giving an explicit basis for the Riemann-Roch space L(lD) for 0 < l ≤ q − 1. These codes then have the full Suzuki group Sz(q) as...

Let $G$ be a finite non-abelian $p$-group and $L(G)$ denotes the absolute center of $G$. Also, let $Aut^{L}(G)$ and $Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $Aut_c(G)=Aut^{L}(G)$. We also characterize all finite non-abelian $p$-groups of order $p^...

Baumslag conjectured in the 1970s that the automorphism tower of a finitely generated free group (free nilpotent group) must be very short. Dyer and Formanek [9] justified the conjecture concerning finitely generated free groups in the “sharpest sense” by proving that the automorphism group Aut(Fn) of a non-abelian free group Fn of finite rank n is complete. Recall that a group G is said to be ...