Semi-automorphisms of groups

Some properties of marginal automorphisms of groups

AbstractLet W be a non-empty subset of a free group. The automorphism of a group G is said to be a marginal automorphism, if for all x in G,x^−1alpha(x) in W^*(G), where W^*(G) is the marginal subgroup of G.In this paper, we give necessary and sufficient condition for a purelynon-abelian p-group G, such that the set of all marginal automorphismsof G forms an elementary abelian p-group.

Some Remarks on Commuting Fixed Point Free Automorphisms of Groups

In this a‌r‌t‌i‌c‌l‌e we will find n‌e‌c‌e‌s‌s‌a‌r‌y and s‌u‌f‌f‌i‌c‌i‌e‌n‌t c‌o‌n‌d‌i‌t‌i‌o‌n‌s for a f‌i‌x‌e‌d  p‌o‌i‌n‌t f‌r‌e‌e autom‌o‌r‌p‌h‌i‌s‌m (f‌p‌f a‌u‌t‌o‌m‌o‌r‌p‌h‌i‌s‌m) o‌f a g‌r‌o‌u‌p t‌o b‌e a c‌o‌m‌m‌u‌t‌i‌n‌g a‌u‌t‌o‌m‌o‌r‌p‌h‌i‌s‌m. F‌o‌r a given prim‌e ‌ we  f‌i‌n‌d t‌h‌e s‌m‌a‌l‌l‌e‌s‌t o‌r‌d‌e‌r o‌f a n‌o‌n a‌b‌e‌l‌i‌a‌n p-g‌r‌o‌u‌p a‌d‌m‌i‌t‌t‌i‌n‌g a c‌o‌m‌m‌u‌t‌i‌n‌g f...

Automorphisms of Coxeter Groups

We compute Aut(W ) for any even Coxeter group whose Coxeter diagram is connected, contains no edges labeled 2, and cannot be separated into more than 2 connected components by removing a single vertex. The description is given explicitly in terms of the given presentation for the Coxeter group and admits an easy characterization of those groups W for which Out(W ) is finite.

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

A Note on Absolute Central Automorphisms of Finite $p$-Groups

Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study  some properties of absolute central automorphisms of a given finite $p$-group.