Related papers: Finite simple automorphism groups of edge-transiti…

Let G be a torsion--free abelian group of finite rank. The automorphism group Aut(G) acts on the set of maximal independent subsets of G. The orbits of this action are the isomorphism classes of indecomposable decompositions of G. G…

We characterize connected tetravalent graphs $\Gamma$ which admit groups $M<H$ of automorphisms such that $\Gamma$ is $M$-half-arc-transitive and $H$-arc-transitive. Examples for each case are constructed, including a counter-example to a…

A graph is called {\em half-arc-transitive} if its full automorphism group acts transitively on vertices and edges, but not on arcs. It is well known that for any prime $p$ there is no tetravalent half-arc-transitive graph of order $p$ or…

We give a geometric characterisation of those groups that arise as fixed subgroups of finite-order untwisted automorphisms of right-angled Artin groups (RAAGs). They are precisely the fundamental groups of a class of compact special cube…

In this article, we focus on a new perspective of automorphisms of complex 2-tori, reviewing previous works from a lattice-theoretic point of view. In particular, we give a classification of families of symplectic and non-symplectic…

We classify K3 surfaces with non-symplectic automorphism of order 16 in full generality. We show that the fixed locus contains only rational curves and points and we completely classify the seven possible configurations. If the…

In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by…

A finite transitive permutation group is said to be 3/2-transitive if all the nontrivial orbits of a point stabilizer have the same size greater than 1. Examples include the 2-transitive groups, Frobenius groups and several other less…

We discuss the possibility of lifting finite subgroups, and in particular finite cyclic subgroups, with respect to the canonical projections between automorphism and outer automorphism groups of free groups, surface groups and their…

An edge-biregular map arises as a smooth normal quotient of a unique index-two subgroup of a full triangle group acting with two edge-orbits. We give a classification of all finite edge-biregular maps on surfaces of negative prime Euler…

We classify minimal pairs (X, G) for smooth rational projective surface X and finite group G of automorphisms on X. We also determine the fixed locus X^G and the quotient surface Y = X/G as well as the fundamental group of the smooth part…

In this paper, we initiate the study of spectrum of the commuting graphs of finite non-abelian groups. We first compute the spectrum of this graph for several classes of finite groups, in particular AC-groups. We show that the commuting…

Any non-abelian finite $p$-group has a non-inner automorphism of order $p$.

There are several examples in the literature of finite non-abelian $p$-groups whose automorphism group is abelian. For some time only examples that were special $p$-groups were known, until Jain and Yadav [JY12] and Jain, Rai and Yadav…

This work presents the conjugacy classes of finite abelian subgroups of the Cremona group of the plane. Using a well-known theory, this problem amounts to the study of automorphism groups of some Del Pezzo surfaces and conic bundles. We…

A graph $\Gamma$ is said to be symmetric if its automorphism group $\rm Aut(\Gamma)$ acts transitively on the arc set of $\Gamma$. In this paper, we show that if $\Gamma$ is a finite connected heptavalent symmetric graph with solvable…

We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).

A longstanding conjecture asserts that every non-abelian finite $p$-group $G$ admits a non-inner automorphism of order $p$. The conjecture is valid for finite $p$-groups of class 2. Here, we prove every finite non-abelian $p$-group $G$ of…

In this paper we describe all the finite almost simple groups whose Gruenberg--Kegel graphs coincide with Gruenberg--Kegel graphs of finite solvable groups.

In this note we show that many subgroups of mapping class groups of infinite-type surfaces without boundary have trivial centers, including all normal subgroups. Using similar techniques, we show that every nontrivial normal subgroup of a…