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Algebraic automorphism groups [PDF]
Illinois Journal of Mathematics, 1975 For an algebraic group G, let W(G) denote the group of all algebraic group automorphisms of G. In this chapter, we examine the possibility of endowing W(G) with the structure of an algebraic group in such a way that G becomes a strict W(G)-variety. The example of a toroid of dimension greater than 1 shows that this is not always possible. However, good
G. Hochschild
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Cluster automorphism groups and automorphism groups of exchange graphs [PDF]
Pacific Journal of Mathematics, 2020 For a coefficient free cluster algebra $\mathcal{A}$, we study the cluster automorphism group $Aut(\mathcal{A})$ and the automorphism group $Aut(E_{\mathcal{A}})$ of its exchange graph $E_{\mathcal{A}}$. We show that these two groups are isomorphic with each other, if $\mathcal{A}$ is of finite type excepting types of rank two and type $F_4$, or if ...
Bin Zhu, Wen Chang
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Rigid automorphisms of linking systems
Forum of Mathematics, Sigma, 2021 A rigid automorphism of a linking system is an automorphism that restricts to the identity on the Sylow subgroup. A rigid inner automorphism is conjugation by an element in the center of the Sylow subgroup.
George Glauberman, Justin Lynd
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Automorphisms of Automorphism Groups of Free Groups [PDF]
Journal of Algebra, 2000 AbstractIf n≥3 and Fn is free of rank n, then Out(Aut(Fn))=Out(Out(Fn))={1}.
Bridson, M, Vogtmann, K
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On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$ [PDF]
International Journal of Group Theory, 2022 A binary triply-even $[98280, 25, 47104]_2$ code invariant under the sporadic simple group ${\rm Co}_1$ is constructed by adjoining the all-ones vector to the faithful and absolutely irreducible 24-dimensional code of length 98280. Using the action of ${\
Bernardo Rodrigues
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On a relation between GAG codes and AG codes
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper, we first give a relationship between generalized algebraic geometry codes (GAG codes) and algebraic geometry codes (AG codes). More precisely, we show that a GAG code is contained (up to isomorphism) in a suitable AG code.
Şenel Engin, Öke Figen
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The Group of Automorphisms of the Pentablock [PDF]
Complex Analysis and Operator Theory, 2014 To appear in ...
Łukasz Kosiński, Łukasz Kosiński
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AUTOMORPHISM GROUPS OF QUANDLES [PDF]
Journal of Algebra and Its Applications, 2012 We prove that the automorphism group of the dihedral quandle with n elements is isomorphic to the affine group of the integers mod n, and also obtain the inner automorphism group of this quandle. In [B. Ho and S. Nelson, Matrices and finite quandles, Homology Homotopy Appl.7(1) (2005) 197–208.], automorphism groups of quandles (up to isomorphisms) of ...
Elhamdadi, Mohamed +2 more
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Automorphism group schemes of bielliptic and quasi-bielliptic surfaces [PDF]
Épijournal de Géométrie Algébrique, 2022 Bielliptic and quasi-bielliptic surfaces form one of the four classes of minimal smooth projective surfaces of Kodaira dimension $0$. In this article, we determine the automorphism schemes of these surfaces over algebraically closed fields of arbitrary ...
Gebhard Martin
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Commensurability of automorphism groups [PDF]
Compositio Mathematica, 2017 We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen–Lenstra heuristics on class groups.
Bartel, Alex, Lenstra, Hendrik W.
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