Related papers: Conjugacy classes of autohomeomorphisms of $\mathb…

A special type of conjugacy classes in symmetric groups is studied and used to answer a question about odd-degree irreducible characters

Let $G$ be a finite group and $N<G$ a normal subgroup with $G/N$ abelian. We show how the conjugacy classes of $G$ in a given coset $qN$ relate to the irreducible characters of $G$ that are not identically $0$ on $qN$. We describe several…

We show that the group generated by by triangular and diagonal conjugations is dense in $\aut(\Omega_2)$ (in the local-uniform topology). Moreover, it is shown that any automorphism of $\Omega_2$ is a local holomorphic conjugation.

We study authomorphisms of $Ind$-groups of polynomial automorphisms (wich are singular) via tame approximations. Such objects were pioneeered in research by B.I.Plotkin We obtain a number of properties of $Aut(Aut(A))$, where $A$ is the…

An automorphism of a graph product of groups is conjugating if it sends each factor to a conjugate of a factor (possibly different). In this article, we determine precisely when the group of conjugating automorphisms of a graph product…

We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }

We construct explicit quantization of semisimple conjugacy classes of the complex orthogonal group SO(N) with non-Levi isotropy subgroups through an operator realization on highest weight modules of the quantum group U_q(so(N)).

We prove that for a number of ultrahomogeneous structures $M$, including those with the free amalgamation property, the powers of the automorphism group ${\rm{Aut}}(M)^n$, $n=1,2,\ldots$, and the group $L_0({\rm{ Aut}}(M))$ of measurable…

We study some extension of a discrete Heisenberg group coming from the theory of loop-groups and find invariants of conjugacy classes in this group. In some cases including the case of the integer Heisenberg group we make these invariants…

Several different areas of group theory, topology and geometry have led to the study of the action of Aut(Fn) | the automorphism group of the free group on n generators | on Hom(Fn;G) when G is either finite,compact or simple Lie group. In…

We construct holomorphic families of proper holomorphic embeddings of $\C^k$ into $\C^n$ ($0<k<n-1$), so that for any two different parameters in the family no holomorphic automorphism of $\C^n$ can map the image of the corresponding two…

We determine which simple algebraic groups of type $^3D_4$ over arbitrary fields of characteristic different from 2 admit outer automorphisms of order 3, and classify these automorphisms up to conjugation. The criterion is formulated in…

We introduce two refinements of the class of $5/2$-groups, inspired by the classes of automorphism groups of configurations and automorphism groups of unit circulant digraphs. We show that both of these classes have the property that any…

We give several algorithms addressing computations of intersections of conjugate subgroups.

Let $A$ be a finite-dimensional (Artinian) Gorenstein algebra, and let $\operatorname{Aut}(A)^{\circ}$ denote the connected component of the identity in the automorphism group of $A$. We introduce a new subclass of Gorenstein algebras and…

In this paper, we study the structure of finite groups with a large number of conjugacy classes of $p$-elements for some prime $p$. As consequences, we obtain some new criteria for the existence of normal $p$-complements in finite groups.

Evidences have suggested that counting representations are sometimes tractable even when the corresponding classification problem is almost impossible, or "wild" in a precise sense. Such counting problems are directly related to matrix…

Let $G$ be a finitely generated polyfree group. If $G$ has nonzero Euler characteristic then we show that $Aut(G)$ has a finite index subgroup in which every automorphism has infinite Reidemeister number. For certain $G$ of length 2, we…

Given any connected compact orientable surface, a pair of mapping classes are said to be procongruently conjugate if they induce a conjugate pair of outer automophisms on the profinite completion of the fundamental group of the surface. For…

Let $X[n]$ be the Fulton-MacPherson compactification of the configuration space of $n$ ordered points on a smooth projective variety $X$. We prove that if either $n\neq 2$ or $\dim(X)\geq 2$, then the connected component of the identity of…