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Automorphism Groups of Nilpotent Groups
Bulletin of the London Mathematical Society, 1989Let \({\mathfrak X}\) 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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Automorphism groups of superextensions of groups
, 2017The 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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Noetherian Automorphisms of Groups
Mediterranean Journal of Mathematics, 2005An automorphism α of a group G is called a noetherian automorphism if for each ascending chain $$ X_1 < X_2 < \ldots < X_n < X_{n + 1} < \ldots $$ of subgroups of G there is a positive integer m such that \(X_n^{\alpha} = X_n \) for all n ≥ m. The structure of the group of all noetherian automorphisms of a group is investigated in this paper.
DE GIOVANNI, FRANCESCO, DE MARI, FAUSTO
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Bulletin of the London Mathematical Society, 1998
Let \(A\) be a group of automorphisms of the finite group \(G\) such that \((|A|,|G|)=1\). The authors prove that \(|A|0\), groups \(G\) and \(A\leq\Aut(G)\) can be found such that \((|A|,|G|)=1\) and \(|A|>|G|^{2-\varepsilon}\). Furthermore, if \(A\) is nilpotent of class at most 2, then \(|A|
Pálfy, P. P., Pyber, L.
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Let \(A\) be a group of automorphisms of the finite group \(G\) such that \((|A|,|G|)=1\). The authors prove that \(|A|0\), groups \(G\) and \(A\leq\Aut(G)\) can be found such that \((|A|,|G|)=1\) and \(|A|>|G|^{2-\varepsilon}\). Furthermore, if \(A\) is nilpotent of class at most 2, then \(|A|
Pálfy, P. P., Pyber, L.
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Automorphism groups of Gabidulin-like codes
arXiv.org, 2016Let K/k be a cyclic Galois extension of degree $${\ell}$$ℓ and $${\theta }$$θ a generator of Gal(K/k). For any $${v=(v_1, \ldots, v_m)\in K^{m}}$$v=(v1,…,vm)∈Km such that v is linearly independent over k, and any $${1\leq d < m }$$1 ...
Dirk Liebhold, G. Nebe
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Automorphism Groups of Formal Matrix Rings
Journal of Mathematical Sciences, 2021P. Krylov, A. Tuganbaev
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Automorphism groups of nilpotent groups
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 \(1\triangleleft Z(G)\triangleleft G\)
Braun, Gábor, Göbel, Rüdiger
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Automorphism groups of quandles arising from groups
, 2016Let G be a group and $$\varphi \in {\text {Aut}}(G)$$φ∈Aut(G). Then the set G equipped with the binary operation $$a*b=\varphi (ab^{-1})b$$a∗b=φ(ab-1)b gives a quandle structure on G, denoted by $${\text {Alex}}(G, \varphi )$$Alex(G,φ), and called the ...
V. Bardakov, Pinka Dey, Mahender Singh
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Automorphism Groups of Geometrically Represented Graphs
Symposium on Theoretical Aspects of Computer Science, 2014We describe a technique to determine the automorphism group of a geometrically represented graph, by understanding the structure of the induced action on all geometric representations.
Pavel Klavík, Peter Zeman
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Automorphism groups of metabelian groups
Mathematical Notes of the Academy of Sciences of the USSR, 1987Translation from Mat. Zametki 41, No.1, 9-22 (Russian) (1987; Zbl 0617.20017).
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