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Agrarian and ℓ 2 -Betti numbers of locally indicable groups, with a twist. [PDF]

Math Ann
Kielak D, Sun B.
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Automorphisms of Automorphism Group of Dihedral Groups

Creative Mathematics and Informatics, 2023
The automorphism group of a Dihedral group of order 2n is isomorphic to the holomorph of a cyclic group of order n. The holomorph of a cyclic group of order n is a complete group when n is odd. Hence automorphism groups of Dihedral groups of order 2n are its own automorphism groups whenever n is odd. In this paper, we prove that the result is also true
Sajikumar, Sadanandan, Vinod, Sivadasan, Biju, Gopinadhan Sathikumari   +2 more
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Automorphism Groups of Countable Structures

Coarse Geometry of Topological Groups, 2021
Suppose M is a countable first-order structure with a ‘rich’ automorphism group Aut(M). We will study Aut(M) both as a group and as a topological group, where the topology is that of pointwise convergence.
D. Evans
semanticscholar   +1 more source

On the Group of Automorphisms of a Group

The American Mathematical Monthly, 2011
AbstractThis note gives a generalization of the classical result asserting that if the center of a group G is trivial, then so is the center of its automorphism group Aut(G).
Marian Deaconescu, Gary L. Walls
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ON THE CENTRE OF THE AUTOMORPHISM GROUP OF A GROUP

Bulletin of the Australian Mathematical Society, 2015
If the centre of a group $G$ is trivial, then so is the centre of its automorphism group. We study the structure of the centre of the automorphism group of a group $G$ when the centre of $G$ is a cyclic group. In particular, it is shown that the exponent of $Z(\text{Aut}(G))$ is less than or equal to the exponent of $Z(G)$ in this case.
Farrokhi D. G., M., Moghaddam, Mohammad Reza R.   +1 more
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Automorphism groups of superextensions of groups

, 2017
The superextension $\lambda(X)$ of a set $X$ consists of all maximal linked families on $X$. Any associative binary operation $*: X\times X \to X$ can be extended to an associative binary operation $*: \lambda(X)\times\lambda(X)\to\lambda(X)$.
T. Banakh, Volodymyr Gavrylkiv
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The Automorphism Groups of the Braid Groups

American Journal of Mathematics, 1981
In the first of two papers published in the Annals in 1947 [3] Emil Artin mentioned the problem of determining all automorphisms of the braid groups (of the Euclidean plane), and in the second [4] took a first step towards a solution. The main result of this paper is a complete determination of these automorphism groups: the outer automorphism group is
Dyer, Joan L., Grossman, Edna K.
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Automorphism Groups of Nilpotent Groups

Bulletin of the London Mathematical Society, 1989
Let \({\mathfrak X}\) denote the class of all finitely generated torsion-free nilpotent groups G such that the derived factor group G/G' is torsion- free. For G in \({\mathfrak X}\), let Aut *(G) denote the group of automorphisms of G/G' induced by the automorphism group of G. If G/G' has rank n and we choose a \({\mathbb{Z}}\)-basis for G/G' then Aut *
Bryant, R. M., Papistas, A.
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Automorphisms of the Gersten Group

Siberian Mathematical Journal, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dudkin, F. A., Shaporina, E. A.
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Automorphism Groups

Springer Undergraduate Mathematics Series, 2020
. This paper aims to establish the geometrical finite-ness for the natural isometric actions of (birational) automorphism groups on the hyperbolic spaces for K3 surfaces, Enriques surfaces, Coble surfaces, and irreducible symplectic varieties.
S. Dougherty
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