Related papers: Normalizers and centralizers of cyclic subgroups g…

Let $G$ be a group and let ${\mathcal G}$ be a free factor system of $G$, namely a free splitting of $G$ as $G=G_1*\dots*G_k*F_r$. In this paper, we study the set of train track points for ${\mathcal G}$-irreducible automorphisms $\phi$…

In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property holds for these groups. Using our methods we show that the…

We have results about the centralizer.

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a…

Let $G=C_{p^n}$ be a finite cyclic p-group, and let $Hol(G)$ denote its holomorph. In this work, we find and characterize the regular subgroups of $Hol(G)$ that are mutually normalizing each other in the permutation group $Sym(G)$. We…

Let G be any finitely generated infinite group. Denote by K(G) the FC-centre of G, i.e., the subgroup of all elements of G whose centralizers are of finite index in G. Let QI(G) denote the group of quasi-isometries of G with respect to word…

We show that a surjective homomorphism $\varphi \colon \Gamma \to K$ of (discrete) groups induces an isomorphism $H^\bullet_b(K; V) \to H^\bullet_b(\Gamma; \varphi^{-1} V)$ in bounded cohomology for all dual normed $K$-modules $V$ if and…

In this article, we study the fixed-point subgroups of the solvable Baumslag-Solitar groups $\BS(1,n)= \langle a, t \mid t a t^{-1} = a^{n} \rangle$, $n>1$ of automorphisms and endomorphisms. We also investigate the stabilizers of subgroups…

A skew morphism of a finite group $G$ is an element $\varphi$ of $\mathrm{Sym}(G)$ preserving the identity element of $G$ and having the property that for each $a\in G$ there exists a non-negative integer $i_a$ such that…

We show that every finite group $T$ is isomorphic to a normalizer quotient $N_{S_n}(H)/H$ for some $n$ and a subgroup $H\leq S_n$. We show that this holds for all large enough $n\ge n_0(T)$ and also with $S_n$ replaced by $A_n$. The two…

Let $\phi \in \mbox{Out}(F_n)$ be a free group outer automorphism that can be represented by an expanding, irreducible train-track map. The automorphism $\phi$ determines a free-by-cyclic group $\Gamma=F_n \rtimes_\phi \mathbb Z,$ and a…

It is well known that the normaliser of a parabolic subgroup of a finite Coxeter group is the semidirect product of the parabolic subgroup by the stabiliser of a set of simple roots. We show that a similar result holds for all finite…

We study the minimally displaced set of irreducible automorphisms of a free group. Our main result is the co-compactness of the minimally displaced set of an irreducible automorphism with exponential growth $\phi$, under the action of the…

By using a cocycle generated by the step function $\varphi_{\beta, \gamma} = 1_{[0, \beta]} - 1_{[0, \beta]} (. + \gamma)$ over an irrational rotation $x \to x + \alpha \mod 1$, we present examples which illustrate different aspects of the…

We study a class of $\Z^{d}$-substitutive subshifts, including a large family of constant-length substitutions, and homomorphisms between them, i.e., factors modulo isomorphisms of $\Z^{d}$. We prove that any measurable factor map and even…

Let $\T$ be a $2$-torsion free triangular ring and let $\varphi:\T\rightarrow \T$ be an additive map. We prove that if $\A \varphi(\B)+\varphi(\B)\A=0$ whenever $\A,\B\in \T$ are such that $\A\B=\B\A=0$, then $\varphi$ is a centralizer. It…

Let $H$ be a connected semisimple linear algebraic group defined over $\mathbb C$ and $X$ a compact connected Riemann surface of genus at least three. Let ${\mathcal M}'_X(H)$ be the moduli space parametrising all topologically trivial…

A generalized Baumslag-Solitar group (GBS group) is a finitely generated group $G$ which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that Out(G) either contains non-abelian free groups or is virtually…

We study non conventional superconductivity on a ladder, improving the predictions of the Hubbard model. The determination of the Fermi surface, in 2 or 3 dimensions, remains a very hard task, but it is exactly solvable for a single ladder.…

Let 1-> H -> G _> Q -> 1 be an exact sequence of groups. In the paper of R. Oliver and J. Ventura, TAMS,362(2009), the following exact sequence was developed for centric extensions, i.e the centralizer of H in G is contained in H, 0->…