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Automorphism groups of nilpotent groups [PDF]

Archiv der Mathematik, 2003
\textit{M. Dugas} and \textit{R. Göbel} [Arch. Math. 54, No. 4, 340-351 (1990: Zbl 0703.20033)] proved the following result: if \(H\) is any group, there is a torsion-free nilpotent group \(G\) of class \(2\) such that \(\Aut(G)=H\ltimes\text{Stab}(G)\), where \(\text{Stab}(G)\) is the stability group of the series \(1\triangleleft Z(G)\triangleleft G\)
Rüdiger Göbel, Gábor Braun
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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 groups

Acta Applicandae Mathematicae, 1992
This is a survey article. The main sections are as follows: Automorphisms of free groups, including Gersten's Theorem and related results. The influence on a group of restricting its automorphism group. Automorphisms of soluble groups, including automorphisms of nilpotent and polycyclic groups and work related to that of Bachmuth and Mochizuki on ...
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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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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
Joan L. Dyer, Edna K. Grosssman
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Automorphism groups of metabelian groups [PDF]

Mathematical Notes of the Academy of Sciences of the USSR, 1987
Translation from Mat. Zametki 41, No.1, 9-22 (Russian) (1987; Zbl 0617.20017).
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The Automorphism Group of a Lie Group

Transactions of the American Mathematical Society, 1952
Introduction. The group A (G) of all continuous and open automorphisms of a locally compact topological group G may be regarded as a topological group, the topology being defined in the usual fashion from the compact and the open subsets of G (see ?1). In general, this topological structure of A (G) is somewhat pathological.
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On commuting automorphisms of groups

Archiv der Mathematik, 2002
Let \(A(G)=\{\alpha\in\Aut(G)\mid x\alpha(x)=\alpha(x)x\) for all \(x\) in \(G\}\) and \(\text{Cent}(G)=\{\alpha\in\Aut(G)\mid\alpha(C(x))=C(x)\) for all \(x\) in \(G\}\). The authors show that \(A(G)\) is not necessarily a subgroup of \(\Aut(G)\) but \(\alpha^2\in\text{Cent}(G)\) for all \(\alpha\in A(G)\) (Lemma 2.4(i)); if \(G\) is Noetherian, then \
Deaconescu, M., Silberberg, G., Walls, Gary L.   +2 more
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