相关论文: Class-preserving automorphisms and the normalizer …

Let G be a torsion--free abelian group of finite rank. The automorphism group Aut(G) acts on the set of maximal independent subsets of G. The orbits of this action are the isomorphism classes of indecomposable decompositions of G. G…

In the paper we study the semigroup $\mathscr{C}_{\mathbb{Z}}$ which is a generalization of the bicyclic semigroup. We describe main algebraic properties of the semigroup $\mathscr{C}_{\mathbb{Z}}$ and prove that every non-trivial…

After discussing some basic facts about generalized module maps, we use the representation theory of the algebra of adjointable operators on a Hilbert B-module E to show that the quotient of the group of generalized unitaries on E and its…

We study properties of a group, abelian group, ring, or monoid $B$ which (a) guarantee that every homomorphism from an infinite direct product $\prod_I A_i$ of objects of the same sort onto $B$ factors through the direct product of finitely…

Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this note, we give some characterizations for normality of H in G. As a consequence we get a very short and elementary proof of the Main Theorem of…

By an automorphism of a topological group G we mean an isomorphism of G onto itself which is also a homeomorphism. In this article, we study the automorphism group Aut(G) of a dense subgroup G of R^n, n>=1. We show that Aut(G) can be…

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…

If H is a flat group of automorphisms of finite rank n of a totally disconnected, locally compact group G, then each orbit of H in the metric space B(G) of compact, open subgroups of G is quasi-isometric to n-dimensional euclidean space. In…

Let $K$ be a field and $f:\mathbb{P}^N \to \mathbb{P}^N$ a morphism. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group $\text{PGL}_{N+1}$. The group of automorphisms, or…

Let $G$ be a group. The central automorphism group $Aut_c(G)$ of $G$ is the centralizer of $Inn(G)$ the subgroup of $Aut(G)$ of inner automorphisms. There is a one to one map $ \sigma \mapsto h_\sigma$ from the set $Aut_c(G)$ onto the set…

For a group $G$, a {\it normalizer covering} of $G$ is a finite set of proper normalizers of some subgroups of $G$ whose union is $G$. We study $p$-groups ($p$ a prime) without a normalizer covering. As an application, we determine some…

Let $A$ be the set of elements in an algebraic function field $K$ over ${\mathbb F}_q$ which are integral outside a fixed place $\infty$. Let $G=GL_2(A)$ be a {\it Drinfeld modular group}. The normalizer of $G$ in $GL_2(K)$, where $K$ is…

$\textit{Normalizer circuits}$ [1,2] are generalized Clifford circuits that act on arbitrary finite-dimensional systems $\mathcal{H}_{d_1}\otimes ... \otimes \mathcal{H}_{d_n}$ with a standard basis labeled by the elements of a finite…

We show that several classes of groups G of PL-homeomorphisms of the real line admit non-trivial homomorphisms from G to the additive group of reals that are fixed by every automorphism of G. The classes of groups enjoying the stated…

We prove that a finitely generated pro-$p$ group acting on a pro-$p$ tree $T$ with procyclic edge stabilizers is the fundamental pro-$p$ group of a finite graph of pro-$p$ groups with edge and vertex groups being stabilizers of certain…

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable relatively hyperbolic group is residually finite. As a direct consequence, we obtain that the outer automorphism group of a limit…

Let G be a countable discrete group and let M be a smooth proper cocompact G-manifold without boundary. The Euler operator defines via Kasparov theory an element, called the equivariant Euler class, in the equivariant K-homology of M. The…

In this paper we define and investigate a class of groups characterized by a representation-theoretic property we call purely noncommuting or PNC. This property guarantees that the group has an action on a smooth projective variety with…

Let $G$ be a Lie group, with an invariant non-degenerate symmetric bilinear form on its Lie algebra, let $\pi$ be the fundamental group of an orientable (real) surface $M$ with a finite number of punctures, and let $\bold C$ be a family of…

There are various results in the literature which are part of the general philosophy that a finite group for which a certain parameter (for example, the number of conjugacy classes or the maximum number of elements inverted, squared or…