We determine the quantum automorphism groups of finite graphs. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group D4.

In this paper, we describe all automorphism-liftable torsion modules over non-primitive hereditary Noetherian prime rings. We also study non-torsion not necessarily commutative Dedekind

Let F be a perfect field and M(F ) the nonassociative simple Moufang loop consisting of the units in the (unique) split octonion algebra O(F ) modulo the center. Then Aut(M(F )) is equal to G2(F )o Aut(F ). In particular, every automorphism of M(F ) is induced by a semilinear automorphism of O(F ). The proof combines results and methods from geometrical loop theory, groups of Lie type and compo...

A circulant (di)graph is a (di)graph on n vertices that admits a cyclic automorphism of order n. This paper provides a survey of the work that has been done on finding the automorphism groups of circulant (di)graphs, including the generalisation in which the edges of the (di)graph have been assigned colours that are invariant under the aforementioned cyclic automorphism. Mathematics Subject Cla...

Let F = (F1, . . . , Fn) : Cn → Cn be any polynomial mapping. By multidegree of F, denoted mdegF, we call the sequence of positive integers (deg F1, . . . , degFn). In this paper we addres the following problem: for which sequence (d1, . . . , dn) there is an automorphism or tame automorphism F : Cn → Cn with mdegF = (d1, . . . , dn). We proved, among other things, that there is no tame automor...

‎‎in this paper we determine all finite $2$-groups of‎ ‎class $2$ in which every automorphism of order $2$ leaving the frattini subgroup elementwise fixed is inner‎.

we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.

We prove that every automorphism of the category of free Lie algebras is a semi-inner automorphism. This solves the problem 3.9 from [19] for Lie algebras.

We construct some codes, designs and graphs that have the first or second Janko group, J1 or J2, respectively, acting as an automorphism group. We show computationally that the full automorphism group of the design or graph in each case is J1, J2 or J̄2, the extension of J2 by its outer automorphism, and we show that for some of the codes the same is true.

We give equivalent and sufficient criteria for the automorphism group of a complete toric variety, respectively a Gorenstein toric Fano variety, to be reductive. In particular we show that the automorphism group of a Gorenstein toric Fano variety is reductive, if the barycenter of the associated reflexive polytope is zero. Furthermore a sharp bound on the dimension of the reductive automorphism...