Related papers: Conjugacy problem in groups with quadratic Dehn fu…

We study the Diophantine problem, i.e. the decision problem of solving systems of equations, for some families of one-relator groups, and provide some background for why this problem is of interest. The method used is primarily the…

In this note, we determine the finite groups whose poset of conjugacy classes of subgroups has breaking points. This leads to a new characterization of the generalized quaternion $2$-groups. A generalization of this property is also…

We give a comprehensive description of conjugation quandles and their connectedness. In this context, we find a characterization of Hayashi's conjecture (2013) in terms of a centrality condition of groups. This condition is thus a…

In this paper we formulate some conjectures in sub-Riemannian geometry concerning a characterisation of the Koranyi-Kaplan ball in a group of Heisenberg type through the existence of a solution to suitably overdetermined problems. We prove…

This paper initiates the study of effective twisted conjugacy separability for finitely generated groups, which measures the complexity of separating distinct twisted conjugacy classes via finite quotients. The focus is on nilpotent groups,…

In a recent paper, Bacher and de la Harpe study the conjugacy growth series of finitary permutation groups. In the course of studying the coefficients of a series related to the finitary alternating group, they introduce generalized…

We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight line programs defined…

This is the final draft, containing very minor proof-reading corrections. Let G in SL(n,\C) be a finite subgroup and \fie: Y -> X = \C^n/G any resolution of singularities of the quotient space. We prove that crepant exceptional prime…

We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…

We show that the twisted conjugacy problem is solvable for large-type Artin groups whose outer automorphism group is finite, generated by graph automorphisms and the global inversion. This includes XXXL Artin groups whose defining graph is…

Let $G$ be one of the finite general linear, unitary, symplectic or orthogonal groups over finite fields of odd order. We find the cardinality of the fibers of the square map at a given generic element. Using this we find the number of real…

The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset GL(n,{\bf C})$ or $c_j\subset gl(n,{\bf C})$ so that there…

In this paper we introduce and study the conjugacy ratio of a finitely generated group, which is the limit at infinity of the quotient of the conjugacy and standard growth functions. We conjecture that the conjugacy ratio is $0$ for all…

In 1960, L\'{a}szl\'{o} Fuchs posed the problem of determining which groups $G$ are realizable as the group of units in some ring $R$. In \cite{chebolu2022fuchs}, we investigated the following variant of Fuchs' problem, for abelian groups:…

We prove that, for a finitely generated residually finite group, having solvable word problem is not a sufficient condition to be a subgroup of a finitely presented residually finite group. The obstruction is given by a residually finite…

This work presents the conjugacy classes of finite abelian subgroups of the Cremona group of the plane. Using a well-known theory, this problem amounts to the study of automorphism groups of some Del Pezzo surfaces and conic bundles. We…

Modelled on efficient algorithms for solving the conjugacy problem in hyperbolic groups, we define and study the permutation conjugacy length function. This function estimates the length of a short conjugator between words $u$ and $v$, up…

We study an analogue of the conjugacy growth function in finitely generated groups: the automorphic growth function. This counts the number of automorphic orbits that intersect the ball of radius $n$ in the group. We show that this is not a…

Let $G$ be a finite group and let $p$ be a prime. In this paper, we study the structure of finite groups with a large number of $p$-regular conjugacy classes or, equivalently, a large number of irreducible $p$-modular representations. We…

This is a study of terminating and ill-defined Gauss hypergeometric functions. Corresponding hypergeometric equations have a degenerate set of of 24 Kummer's solutions. We describe those solutions and relations between them.