Related papers: Automorphisms groups for $p$-cyclic covers of the …

We study covering graphs of the Paley graph associated to a finite field of characteristic p in the case where the covering transformation group is cyclic of prime order distinct from p. When the field has q = p elements, we show that the…

Given a smooth and separated K(pi,1) variety X over a field k, we associate a "cycle class" in etale cohomology with compact supports to any continuous section of the natural map from the arithmetic fundamental group of X to the absolute…

Let $G$ be a connected reductive group over a totally real field $F$ which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p between the space of arbitrary automorphic forms on $G(\mathbb…

We study certain subgroups of the full group of Hopf algebra automorphisms of a biproduct. In the process interesting subgroups of certain permutation groups come into play.

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…

Let G be a cyclic p-group of order p^n acting by automorphisms on a (non-necessarily commutative) ring R. Suppose there is an element x in R such that (1 + t + ... + t^{p-1})(x) = 1, where t is an element of order p in G. We show how to…

It is well known that every finite subgroup of automorphism group of polynomial algebra of rank 2 over the field of zero characteristic is conjugated with a subgroup of linear automorphisms. We prove that it is not true for an arbitrary…

We classify the dessins $\mathcal D$ for which the automorphism group $G$ acts primitively and faithfully on the points over one of the three critical values (without loss of generality the black vertices in the usual bipartite map…

We study the Picard groups of moduli spaces of smooth complex projective curves that have a group of automorphisms with a prescribed topological action. One of our main tools is the theory of symmetric mapping class groups. In the first…

It is shown that a necessary condition for an abstract group G to be the full automorphism group of a Hamiltonian cycle system is that G has odd order or it is either binary, or the affine linear group AGL(1; p) with p prime. We show that…

We study in detail the profinite group G arising as geometric \'etale iterated monodromy group of an arbitrary quadratic polynomial over a field of characteristic different from two. This is a self-similar closed subgroup of the group of…

In this paper we give an effective criterion as to when a prime number p is the order of an automorphism of a smooth cubic hypersurface of P^{n+1}, for a fixed n > 1. We also provide a computational method to classify all such hypersurfaces…

An automorphism of a graph $G$ with $n$ vertices is a bijective map $\phi$ from $V(G)$ to itself such that $\phi(v_i)\phi(v_j)\in E(G)$ $\Leftrightarrow$ $v_i v_j\in E(G)$ for any two vertices $v_i$ and $v_j$ of $G$. Denote by…

Let $k$ be an algebraically closed field of characteristic $p$ and let $X$ the projective line over $k$ with three points removed. We investigate which finite groups $G$ can arise as the monodromy group of finite \'{e}tale covers of $X$…

Every semidirect product of groups $K\rtimes H$ has size $\left | K \right | \cdot \left | H\right |$, yet the size of such a group's automorphism group varies with the chosen action of $H$ on $K$. This paper will explore groups of the form…

Frucht showed that, for any finite group $G$, there exists a cubic graph such that its automorphism group is isomorphic to $G$. For groups generated by two elements we simplify his construction to a graph with fewer nodes. In the general…

Let $\mathcal{L}$ be a finite-dimensional semisimple Lie algebra of rank $N$ over an algebraically closed field of characteristic $0$. Associated to $\mathcal{L}$ is a family of polynomial folding maps…

When the standard representation of a crystallographic Coxeter group is reduced modulo an odd prime p, one obtains a finite group G^p acting on some orthogonal space over Z_p . If the Coxeter group has a string diagram, then G^p will often…

Let $k$ be an algebraically closed field of characteristic zero, $F$ be an algebraically closed extension of $k$ of transcendence degree one, and $G$ be the group of automorphisms over $k$ of the field $F$. The purpose of this note is to…

We characterize all finite p-groups G of order p^n(n\leq 6), where p is a prime for n\leq 5 and an odd prime for n = 6, such that the center of the inner automorphism group of G is equal to the group of central automorphisms of G.