Related papers: Expansive Automorphisms on Locally Compact Groups

We study automorphisms $\alpha$ of a totally disconnected, locally compact group $G$ which are expansive in the sense that, for some identity neighbourhood $U$, the sets $\alpha^n(U)$ (for integers $n$) intersect in the trivial group.…

For a locally compact metrizable group $G$, we consider the action of ${\rm Aut}(G)$ on ${\rm Sub}_G$, the space of all closed subgroups of $G$ endowed with the Chabauty topology. We study the structure of groups $G$ admitting automorphisms…

A connected Lie group admitting an expansive automorphism is known to be nilpotent, but all nilpotent Lie groups do not admit expansive automorphism. In this article, we find sufficient conditions for a class of nilpotent Lie groups to…

We investigate some situation in which automorphisms of a group G are uniquely determined by their restrictions to a proper subgroup H. Much of the paper is devoted to studying under which additional hypotheses this property forces G to be…

To any automorphism, $\alpha$, of a totally disconnected, locally compact group, $G$, there is associated a compact, $\alpha$-stable subgroup of $G$, here called the \emph{nub} of $\alpha$, on which the action of $\alpha$ is topologically…

Let $\alpha$ be a coprime automorphism of a group $G$ of prime order and let $P$ be an $\alpha$-invariant Sylow $p$-subgroup of $G$. Assume that $p\notin \pi(C_G(\alpha))$. Firstly, we prove that $G$ is $p$-nilpotent if and only if…

We show that with few exceptions every local isometric automorphism of the group algebra $L^p(G)$ of a compact group $G$ is an isometric automorphism.

A group, $\fl{H}$, of automorphisms of a totally disconnected locally compact group, $G$, is flat if there is a compact open $U\leq G$ such that the index $[\alpha(U):U\cap \alpha(U)]$ is mininimized for every $\alpha\in\fl{H}$. The…

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally…

Let $G$ be a finite group admitting a coprime automorphism $\alpha$. Let $J_G(\alpha)$ denote the set of all commutators $[x,\alpha]$, where $x$ belongs to an $\alpha$-invariant Sylow subgroup of $G$. We show that $[G,\alpha]$ is soluble or…

Let G be a Lie group over a local field of positive characteristic which admits a contractive automorphism f (i.e., the forward iterates f^n(x) of each group element x converge to the neutral element 1). We show that then G is a torsion…

We show that the endomorphisms of a compact connected group that extend to endomorphisms of every compact overgroup are precisely the trivial one and the inner automorphisms; this is an analogue, for compact connected groups, of results due…

The paper is devoted to the study of local derivations and automorphisms of nilpotent Lie algebras. Namely, we proved that nilpotent Lie algebras with indices of nilpotency $3$ and $4$ admit local derivation (local automorphisms) which is…

For a locally compact group $G$, we study the distality of the action of automorphisms $T$ of $G$ on ${\rm Sub}_G$, the compact space of closed subgroups of $G$ endowed with the Chabauty topology. For a certain class of discrete groups $G$,…

We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their…

Let G be a free group in a variety of groups, but G is not absolutely free. We prove that the group of automorphisms Aut(G) is linear iff G is a virtually nilpotent group.

We consider expansive group actions on a compact metric space containing a special fixed point denoted by $0$, and endomorphisms of such systems whose forward trajectories are attracted toward $0$. Such endomorphisms are called…

For a real, non-singular, 2-step nilpotent Lie algebra $\mathfrak{n}$, the group \Aut(\mathfrak{n})/\Aut_0(\mathfrak{n})$, where $\Aut_0(\mathfrak{n})$ is the group of automorphisms which act trivially on the center, is the direct product…

Let F be a local field of positive characteristic, and let G be either a Heisenberg group over F, or a certain (nonabelian) two-dimensional unipotent group over F. If H is an arithmetic subgroup of G, we provide an explicit description of…

It is well known that every locally compact abelian group L can be decomposed as L_1 \oplus R^n, where L_1 contains a compact-open subgroup. In this paper, we use this decomposition to study the topological group Aut(L) of automorphisms of…