Related papers: Aut(F2) puzzles

In this article we analyze the structure of $2$-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting…

This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a…

We study, from a constructive computational point of view, the techniques used to solve the conjugacy problem in the "generic" lattice-ordered group Aut(R) of order automorphisms of the real line. We use these techniques in order to show…

This paper contains results related to synthesis and presentation of abstract automata by fragments of behaviour and investigates the structure of the classes of finite connected initial output-less automata specified by systems of defining…

This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…

We develop an analogue of the Birman exact sequence for the Torelli subgroup of Aut(F_n). This builds on earlier work of the authors who studied an analogue of the Birman exact sequence for the entire group Aut(F_n). These results play an…

This is the third one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups in odd dimension.

This is the fifth one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups of plus type.

The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric…

This is a short survey paper, partly meant as a research announcement. Its purpose is to highlight some aspects of the interplay between quantales, inverse semigroups, and groupoids. Many of the results mentioned have not yet been presented…

The notion of quadratic maps between arbitrary groups appeared at several places in the literature on quadratic algebra. Here a unified extensive treatment of their properties is given; the relation with a relative version of Passi's…

A set-theoretic solution to the Pentagon Equation can be described as a \emph{pentagon} algebra $(S, \cdot, \ast)$ such that $(S, \cdot)$ is a semigroup and the operations $\cdot$ and $\ast$ are related by two additional equations. This…

We develop a theory of generalized presentations of groups. We give generalized presentations of the symmetric group $\Sigma(X)$ for an arbitrary set $X$ and of the automorphism group of the free group of countable rank, $Aut(F_{\omega})$.

We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.

This manuscript provides a more detailed treatment of the material from my lecture series at the 2022 Arizona Winter School on Automorphic Forms Beyond $GL_2$. The main focus of this manuscript is automorphic forms on unitary groups, with a…

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

We study certain subgroups of the full group of Hopf algebra automorphisms of a biproduct. In the process interesting subgroups of certain permutation groups come into play.

With every matching in a graph we associate a group called the matching group. We study this group using the theory of non-positively curved cubed complexes. Our approach is formulated in terms of so-called gliding systems.

In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…

Two new classes of finite automata, called General hexagonal Boustrophedon finite automata and General hexagonal returning finite automata operating on hexagonal grids, are introduced and analyzed. The work establishes the theoretical…