Related papers: Detecting automorphic orbits in free groups
Circulant graphs are a widely studied family of graphs whose members possess varying amounts of symmetry. Although considerable progress has been made in finding the automorphism groups of circulant graphs under certain restrictions, a…
By using a notion of a geometric Dehn twist in $\sharp_k(S^2 \times S^1)$, we prove that when projections of two $\mathbb{Z}$-splittings to the free factor complex are far enough from each other in the free factor complex, Dehn twist…
We present a new algorithm for computing the first discrete homology group of a graph. By testing the algorithm on different data sets of random graphs, we find that it significantly outperforms other known algorithms.
Automated symmetry detection is still a difficult task in 2021. However, it has applications in computer vision, and it also plays an important part in understanding art. This paper focuses on aiding the latter by comparing different…
In this paper, we study some properties of the outer automorphism group of free Burnside groups of large odd exponent. In particular, we prove that it contains free and free abelian subgroups.
We study the automorphism groups attached to a free algebra with multiple, possibly infinitely many, composition laws. As an application, we prove that the automorphism group of finitely generated vertex algebras over noetherian rings are…
We describe the development of the theory of automatic groups. We begin with a historical introduction, define the concepts of automatic, biautomatic and combable groups, derive basic properties, then explain how hyperbolic groups and the…
We give upper bounds on the order of the automorphism group of a simple graph
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.
We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…
For a free group automorphism, we prove that its poset of attracting lamination orbits is a canonical invariant of the associated mapping torus. That is, if a free-by-cyclic group splits as a mapping torus in two different ways, then the…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
We determine the structure of automorphism group or each nonsplit metacyclic 2-group. This completes the work on automorphism groups of metacyclic $p$-groups.
In the mid-1990s, two groups of authors independently obtained classifications of vertex-transitive graphs whose order is a product of two distinct primes. In the intervening years it has become clear that there is additional information…
In this paper we discuss a genetic version (GWA) of the Whitehead's algorithm, which is one of the basic algorithms in combinatorial group theory. It turns out that GWA is surprisingly fast and outperforms the standard Whitehead's algorithm…
We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are…
The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K. Vogtmann's work, have been written about a lot. In…
We previously developed an automatic track scanning system which enables the detection of large-angle nuclear fragments in the nuclear emulsion films of the OPERA experiment. As a next step, we have investigated this system's track…
In this paper, we study group equations with occurrences of automorphisms. We describe equational domains in this class of equations. Moreover, we solve a number of open problem posed in universal algebraic geometry.
In this paper, we compute the second homology groups of the automorphism group of a free group with coefficients in the abelianization of the free group and its dual group except for 2-torsion part, using combinatorial group theory.