on central endomorphisms of a group
نویسندگان
چکیده
let $gamma$ be a normal subgroup of the full automorphism group $aut(g)$ of a group $g$, and assume that $inn(g)leq gamma$. an endomorphism $sigma$ of $g$ is said to be {it $gamma$-central} if $sigma$ induces the the identity on the factor group $g/c_g(gamma)$. clearly, if $gamma=inn(g)$, then a $gamma$-central endomorphism is a {it central} endomorphism. in this article the conditions under which a $gamma$-central endomorphism of a group is an automorphism are investigated.
منابع مشابه
A Remark on Mapping Tori of Free Group Endomorphisms
Proof. It is well-known that the kernels of the powers of φ stabilize (see for example [3]), that is, there exists k > 0 such that ker(φ) = ker(φ) for all n ≥ k. (This easily follows from the stabilization of ranks of the free groups φ(F ) and from Hopficity of finitely generated free groups.) Put N = ker(φ). Then φ factors through to an injective endomorphism φ : F/N → F/N . The group F/N is i...
متن کاملRational Endomorphisms of a Nilpotent Group
Let G be a group. An endomorphism φ of G is called rational if there exist a1, . . . , ar ∈ G and h1, . . . , hr ∈ Z, such that φ(x) = (xa1)1 . . . (xar)r for all x ∈ G. We denote by Endr(G) the group of invertible rational endomorphisms of G. In this note, we prove that G is nilpotent of class c (c ≥ 3) if and only if Endr(G) is nilpotent of class c − 1. Mathematics Subject Classification: 20E...
متن کاملApproximate Innerness and Central Triviality of Endomorphisms
We introduce the notions of approximate innerness and central triviality for endomorphisms on separable von Neumann factors, and we characterize them for hyperfinite factors by Connes-Takesaki modules of endomorphisms and modular endomorphisms which are introduced by Izumi. Our result is a generalization of the corresponding result obtained by KawahigashiSutherland-Takesaki in automorphism case.
متن کاملFixed Points of Endomorphisms of a Free Metabelian Group
We consider IA-endomorphisms (i.e. Identical in Abelianization) of a free metabelian group of finite rank, and give a matrix characterization of their fixed points which is similar to (yet different from) the well-known characterization of eigenvectors of a linear operator in a vector space. We then use our matrix characterization to elaborate several properties of the fixed point groups of met...
متن کاملThe density of injective endomorphisms of a free group
We show that among the endomorphisms of the free (non-abelian) group Fr of rank r, the set of monomorphisms (the injective endomorphisms) has density one. This contrasts with the known fact that the set of automorphisms has density zero. We show more generally that in the set of homomorphisms from one free group to another, the set of monomorphisms has density one whereas the set of epimorphism...
متن کاملCircle Endomorphisms, Dual Circles and Thompson’s Group
We construct the dual Cantor set for a degree two expanding map f acting as cover of the circle T onto itself. Then we use the criterion for a continuous function on this Cantor set to be the scaling function of a uniformly asymptotically affine UAA expanding map to show that the scaling function for f descends to a continuous function on a dual circle T∗. We use this representation to view the...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
international journal of group theoryناشر: university of isfahan
ISSN 2251-7650
دوره 4
شماره 3 2015
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023