Related papers: Group Extensions and Automorphism Group Rings

By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…

In this paper, we construct explicitely polynomial automorphisms of affine n-space for certain n. More precisely, we construct algebraic subgroups of the general polynomial group GA_n(k) where k is an arbitrary base ring of characteristic…

We investigate the finite subgroups that occur in the Hamiltonian quaternion algebra over the real subfield of cyclotomic fields. When possible, we investigate their distribution among the maximal orders.

We determine the automorphism group of the split Cartan modular curves $X_{\operatorname{split}}(p)$ for all primes $p$.

A ring R is called an E-ring if the canonical homomorphism from R to the endomorphism ring End(R_Z) of the additive group R_Z, taking any r in R to the endomorphism left multiplication by r turns out to be an isomorphism of rings. In this…

A characterization is given of the subsets of a group that extend to the positive cone of a right order on the group and used to relate validity of equations in lattice-ordered groups (l-groups) to subsets of free groups that extend to…

In this paper, we establish a rigidity result for automorphisms of multiplicative direct products of $D$-rings which are total ring of fraction that have pairwise distinct cardinalities. Under these assumptions, every automorphism acts…

In this note, given a regular Courant algebroid, we compute its group of automorphisms relative to a dissection. We also propose an infinitesimal version and recover examples of the literature.

We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. Our proof includes a structural analysis of finite edge-transitive graphs. In particular, we show that for connected, $K_{h+1}$-minor-free,…

This paper is devoted to a study of the automorphism groups of three series of finite dimensional special odd Hamiltonian superalgebras $\mathfrak{g}$ over a field of prime characteristic. Our aim is to characterize the connections between…

In this article, we explore the problem of determining isomorphisms between the twisted complex group algebras of finite $p$-groups. This problem bears similarity to the classical group algebra isomorphism problem and has been recently…

Given a positive definite even lattice and a commutative ring, there is a standard construction of a lattice vertex algebra over the commutative ring, and it admits a natural grading by non-negative integers. We describe the groups of…

We show that if a group automorphism of a Cremona group of arbitrary rank is also a homeomorphism with respect to either the Zariski or the Euclidean topology, then it is inner up to a field automorphism of the base-field. Moreover, we show…

We investigate the general structure of the automorphism group and the Lie algebra of derivations of a finitely generated vertex operator algebra. The automorphism group is isomorphic to an algebraic group. Under natural assumptions, the…

It is well known that the graph isomorphism problem is polynomial-time reducible to the graph automorphism problem (in fact these two problems are polynomial-time equivalent). We show that, analogously, the group isomorphism problem is…

We classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space and Urysohn sphere, among other related results.

Let G be a finite group and p a prime dividing its order. We define new collections of p-subgroups of G. We study the homotopy relations among them and with the standard collections of p-subgroups. We determine their ampleness and sharpness…

We investigate the algebras of invariants and the properties of the quotient morphism by an action of a finite group scheme in terms of stabilizers of points.

We associate to every quandle $X$ and an associative ring with unity $\mathbf{k}$, a nonassociative ring $\mathbf{k}[X]$ following [3]. The basic properties of such rings are investigated. In particular, under the assumption that the inner…

This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…