Related papers: Classification of groups generated by 3-state auto…
We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…
There is an established bijection between finite-index subgroups Gamma of Gamma(2) and bipartite graphs on surfaces, or, equivalently, certain triples of permutations. We utilize this relationship to study both congruence and noncongruence…
These lecture notes provide an introduction to automorphism groups of graphs. Some special families of graphs are then discussed, especially the families of Cayley graphs generated by transposition sets.
We complete the classification of hyperelliptic threefolds, describing in an elementary way the hyperelliptic threefolds with group $D_4$. These are algebraic and form an irreducible 2-dimensional family. Our paper is fully self-contained.
This paper describes an automatic word classification system which uses a locally optimal annealing algorithm and average class mutual information. A new word-class representation, the structural tag is introduced and its advantages for use…
Elder, Kambites, and Ostheimer showed that if the word problem of a finitely generated group $H$ is accepted by a $G$-automaton for an abelian group $G$, then $H$ is virtually abelian. We give a new, elementary, and purely combinatorial…
Shephard groups are common extensions of Artin and Coxeter groups. They appear, for example, in algebraic study of manifolds. An infinite family of Shephard groups which are not Artin or Coxeter groups is considered. Using techniques form…
This is a book on weighted tree automata. We present the basic definitions and some of the important results in a coherent form with full proofs. The concept of weighted tree automata is part of Automata Theory and it touches the area of…
Group languages are regular languages recognized by finite groups, or equivalently by finite automata in which each letter induces a permutation on the set of states. We investigate the separation problem for this class of languages: given…
We determine the automorphism groups of Koras-Russell threefolds of the second kind. In particular we show that these groups are semi-direct products of two subgroups, one given by the multiplicative group and the other isomorphic to a…
This paper studies Aut(F2) and groups closely related to it from a geometric perspective.
We show that a large number of elementary cellular automata are computationally simple. This work is the first systematic classification of elementary cellular automata based on a formal notion of computational complexity. Thanks to the…
Several questions about the Galois group of field generated by certain one dimensional formal group laws are studied. This is continuation of author's prior article titled 'Field Generated by Division Points of Certain Formal Group Laws -…
We classify all of the groups with twelve or fewer subgroups. This paper is the proof of the entries in a submission to the Online Encyclopedia of Integer Sequences.
This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.
The automorphism groups for the groups of orders $8p$ and $8p^2$ are given. The calculations were done using the programming language CAYLEY. Explicit presentations for both the groups of these orders and their automorphism groups are…
This text aims to provide a self-contained, comprehensive, and reasonably detailed presentation of the theory of Stallings automata and some of its main applications.
The group of 2-by-2 matrices with integer entries and determinant $\pm > 1$ can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional…
We study the properties of the uncountable set of Stewart words. These are Toeplitz words specified by infinite sequences of Toeplitz patterns of the form $\alpha\beta\gamma$, where $\alpha,\beta,\gamma$ is any permutation of the symbols…
In this article, we will show that the automorphism group of any hypergraph is essentially equal to the determinant of some matrix over a ring generated from the set of ground points. With this, we are also able to determine whether two…