An automorphism α of a group G is normal if it fixes every normal subgroup of G setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group G, Inn(G) has finite index in the subgroup Autn(G) of normal automorphisms. If, in addition, G is non-elementary and has no non-trivial finite normal sub...

We show that an effective action of the one-dimensional torus $${\mathbb G}_m$$ on a normal affine algebraic variety X can be extended to semi-direct product G}_m\rightthreetimes {\mathbb G}_a$$ with same general orbit closures if and only there is divisor D consists -fixed points. This result applied study orbits automorphism group $${{\,\mathrm{Aut}\,}}(X)$$ X.

In this paper we prove that if F is a finitely generated free group and φ ∈ Aut(F) is a polynomially growing automorphism then there exists a characteristic subgroup S ≤ F of finite index such that the automorphism of S induced by φ grows polynomially of the same degree as φ. The proof is geometric in nature and makes use of Improved Relative Train Track representatives of free group automorphi...

The main objects of this paper are the graded automorphisms of w x polytopal semigroup rings, i.e., semigroup rings k S where k is a field P Ž and S is the semigroup associated with a lattice polytope P Bruns, P w x. w x Gubeladze, and Trung BGT . The generators of k S correspond bijecP tively to the lattice points in P, and their relations are the binomials representing the affine dependencies...

On the Automorphism Tower of Free Nilpotent Groups Martin Dimitrov Kassabov 2003 In this thesis I study the automorphism tower of free nilpo-tent groups. Our main tool in studying the automorphism tower is to embed every group as a lattice in some Lie group. Using known rigidity results the automorphism group of the discrete group can be embedded into the automorphism group of the Lie group. Th...

We study the class of edge-transitive graphs of square-free order and valency at most k. It is shown that, except for a few special families of graphs, only finitely many members in this class are basic (namely, not a normal multicover of another member). Using this result, we determine the automorphism groups of locally primitive arc-transitive graphs with square-free order.

We give a general criterion for the (bounded) simplicity of the automorphism groups of certain countable structures and apply it to show that the isometry group of the Urysohn space modulo the normal subgroup of bounded isometries is a simple group.

The concept of graph symmetry is explained in terms of the vertex automorphism group, which is a subgroup of the complete vertex permutation group. The automorphism group can be deduced from the automorphism partition of graph vertices. An algorithm is described which constructs the automorphism group of a graph from the automorphism vertex partitioning. The algorithm is useful especially for g...

Automorphism groupS of Hadamard matrices are related to automorphism groups of de.Jigns, and the automorphism groups of the Paley-Hadamard matrices are determined .