The Klein group as an automorphism group without fixed point

An Automorphism of a Free Metabelian Group without Fixed Points

We construct an example of an IA-automorphism of the free metabelian group of rank n ≥ 3 without nontrivial fixed points. That gives a negative answer to the question raised by Shpilrain in [5]. By a result of Bachmuth [1], such an automorphism does not exist if the rank is equal to 2.

THE AUTOMORPHISM GROUP OF FINITE GRAPHS

Let G = (V,E) be a simple graph with exactly n vertices and m edges. The aim of this paper is a new method for investigating nontriviality of the automorphism group of graphs. To do this, we prove that if |E| >=[(n - 1)2/2] then |Aut(G)|>1 and |Aut(G)| is even number.

Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group Or a Unitary Group

The Fermi Liquid as a Renormalization Group Fixed Point

par Guennadi Chitov Thèse présentée au département de Physique en vue de l'obtention du grade de Docteurès sciences (Ph. SUMMARY The renormalization-group (RG) method is applied to study interacting fermions at finite temperature. A model based on the ψ 4-Grassmann effective action with SU(N)-invariant short-range interaction and a rotationally invariant Fermi surface in spatial dimensions d = ...

Splitting the Automorphism Group of an Abelian P-group

Let G be an abelian p-group sum of finite homocyclic groups Gi. Here, we determine in which cases the automorphism group of G splits over kerσ, where σ :Aut(G) → ∏ iAut(Gi/pGi) is the natural epimorphism. 1. Preliminaries Throghout this paper, p is an arbitrary prime and r is a fixed ordinal number. Let G = ⊕i≤rGi be an abelian p-group, such that Gi is an homocyclic group of exponent pi and fin...