Bardakov, V. G. Neshchadim, M. V.
Published in
Algebra and Logic

We study a representation of the virtual braid group VBn into the automorphism group of a free product of a free group and a free Abelian group, proposed by S. Kamada. It is proved that the given representation is equivalent to the representation constructed in [http://arxiv.org/abs/1603.01425]; i.e. the kernels of these representations coincide.

Belousov, I. N. Makhnev, A. A.
Published in
Algebra and Logic

We consider undirected graphs without loops and multiple edges. Previously, V. P. Burichenko and A. A. Makhnev [1] found intersection arrays of distance-regular locally cyclic graphs with the number of vertices at most 1000. It is shown that the automorphism group of a graph with intersection array {15, 12, 1; 1, 2, 15}, {35, 32, 1; 1, 2, 35}, {39,...

Pióro, Konrad
Published in
Mathematica Slovaca

All considered groups are torsion or do not contain infinitely generated subgroups. If such a group G acts transitively on a connected algebra A, then all elements of A have the same stabilizer, so this stabilizer is a normal subgroup (it is also shown that these facts are not true for arbitrary groups). Hence the automorphism group Aut(A) is a hom...

Atabekyan, V. S. Gevorgyan, A. L. Stepanyan, Sh. A.
Published in
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)

In this paper we prove the unique trace property of C*-algebras of n-periodic products of arbitrary family of groups without involutions. We show that the free Burnside groups B(m, n) and their automorphism groups also possess the unique trace property. Also, we show that every countable group is embedded into some 3-generated group with the unique...

Dempwolff, Ulrich
Published in
Advances in Geometry

We determine the automorphism groups of the 2-transitive, bilinear dual hyperovals over 𝔽2 of type D[k] constructed in [6] by the author. Then we characterize the 2-transitive quotients of the Huybrechts dual hyperovals, compute their automorphism groups and give estimates on the number of such quotients.

Kudaĭbergenov, K. Zh.
Published in
Siberian Advances in Mathematics

Within the general model-theoretical framework, we study the small index property and representation of the automorphism group as the union of an increasing chain of proper subsets of a special form.

Donoso, Sebastian Durand, Fabien Maass, Alejandro Petite, Samuel

In this article we study automorphisms of Toeplitz subshifts. Such groups are abelian and any finitely generated torsion subgroup is finite and cyclic. When the complexity is non-superlinear, we prove that the automorphism group is, modulo a finite cyclic group, generated by a unique root of the shift. In the subquadratic complexity case, we show t...

Kovalenko, Sergei Perepechko, Alexander Zaidenberg, Mikhail

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic groups. At the same time, they can be studied from the viewpoint of the combinatorial group theory, so we put a...

Bardakov, V. G. Neshchadim, M. V.
Published in
Algebra and Logic

We study some subgroups of the automorphism group of a free group, their factorizations into a semidirect product, automorphism groups, and adjoint Lie algebras.

Guirardel, Vincent Levitt, Gilbert

The outer automorphism group Out(G) of a group G acts on the set of conjugacy classes of elements of G. McCool proved that the stabilizer $Mc(c_1,...,c_n)$ of a finite set of conjugacy classes is finitely presented when G is free. More generally, we consider the group $Mc(H_1,...,H_n)$ of outer automorphisms $\Phi$ of G acting trivially on a family...