Related papers: On the automorphism groups of Frobenius Groups

This note uses some recent calculations of Conder and Bujalance (on classifying finite index group extensions of Fuchsian groups with abelian quotient and torsion free kernel) in order to determine the full automorphism groups of some cylic…

We establish structure results for Frobenius kernels of automorphism group schemes for surfaces of general type in positive characteristics. It turns out that there are surprisingly few possibilities. This relies on properties of the famous…

The purpose of this paper is to investigate the finite Frobenius groups with "perfect order classes"; that is, those for which the number of elements of each order is a divisor of the order of the group. If a finite Frobenius group has…

Suppose that a Lie algebra $L$ admits a finite Frobenius group of automorphisms $FH$ with cyclic kernel $F$ and complement $H$ of order 2, such that the fixed-point subalgebra of $F$ is trivial and the fixed-point subalgebra of $H$ is…

We investigate the possible structures imposed on a finite group by its possession of an automorphism sending a large fraction of the group elements to their cubes, the philosophy being that this should force the group to be, in some sense,…

Suppose that a finite $p$-group $P$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ that is a cyclic $p$-group and with complement $H$. It is proved that if the fixed-point subgroup $C_P(H)$ of the complement is nilpotent of…

We characterize the groups isomorphic to full automorphism groups of ordered abelian groups. The result will follow from classical theorems on ordered groups adding an argument from proofs used to realize rings as endomorphism rings of…

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.

Suppose that a metacyclic Frobenius group $FH$, with kernel $F$ and complement $H$, acts by automorphisms on a finite group $G$, in such a way that $C_G(F)$ is trivial and $C_G(H)$ is nilpotent. It is known that $G$ is nilpotent and its…

Let A be a supersingular abelian variety over a finite field k. We give an approximate description of the structure of the group A(k) of rational points of A over k in terms of the characteristic polynomial f of the Frobenius endomorphism…

We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.

Let $FH$ be a Frobenius group with kernel $F$ and complement $H$, acting coprimely on the finite solvable group $G$ by automorphisms. We prove that if $C_{G}(H)$ is of Fitting length $n$ then the index of the $n$-th Fitting subgroup…

We show that the equivalence between several possible characterizations of Frobenius algebras, and of symmetric Frobenius algebras, carries over from the category of vector spaces to more general monoidal categories. For Frobenius algebras,…

We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

Suppose that a Lie algebra $L$ admits a finite Frobenius group of automorphisms $FH$ with cyclic kernel $F$ and complement $H$ such that the characteristic of the ground field does not divide $|H|$. It is proved that if the subalgebra…

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.

We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties.…

This article proposes an effective criterion for lifting automorphisms along regular coverings of graphs, with the covering transformation group being any finite abelian group.