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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
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Distortion and the automorphism group of a shift [PDF]
, 2016 The set of automorphisms of a one-dimensional \shift $(X, \sigma)$ forms a countable, but often very complicated, group. For zero entropy shifts, it has recently been shown that the automorphism group is more tame.
Van Cyr, J. Franks, Bryna Kra, S. Petite
semanticscholar +1 more source
The third subgroup of the Andreadakis–Johnson filtration of the automorphism group of a free group
Journal of group theroy, 2019 In this paper, we show that the third subgroup of the Andreadakis–Johnson filtration of the automorphism group of a free group coincides with the third group of the lower central series of the IA-automorphism group.
T. Satoh
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A projective variety with discrete, non-finitely generated automorphism group [PDF]
, 2016 We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.
John Lesieutre
semanticscholar +1 more source
Normal amenable subgroups of the automorphism group of the full shift [PDF]
Ergodic Theory and Dynamical Systems, 2015 We show that every normal amenable subgroup of the automorphism group of the full shift is contained in its center. This follows from the analysis of this group’s Furstenberg topological boundary, through the construction of a minimal and strongly ...
Joshua Frisch, T. Schlank, O. Tamuz
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Automorphism groups of polycyclic-by-finite groups and arithmetic groups [PDF]
, 2005 We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic
A. Borel +40 more
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1-Designs from the group PSL2(59) and their automorphism groups [PDF]
Mathematics Interdisciplinary Research, 2018 In this paper, we consider the projective special linear group PSL2(59) and construct some 1-designs by applying the Key-Moori method on PSL2(59). Moreover, we obtain parameters of these designs and their automorphism groups.
Reza Kahkeshani
doaj +1 more source
The automorphism group of a minimal shift of stretched exponential growth [PDF]
, 2016 The group of automorphisms of a symbolic dynamical system is countable, but often very large. For example, for a mixing subshift of finite type, the automorphism group contains isomorphic copies of the free group on two generators and the direct sum of ...
Bryna Kra, Van Cyr
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THE AUTOMORPHISM GROUP OF A SHIFT OF LINEAR GROWTH: BEYOND TRANSITIVITY [PDF]
Forum of Mathematics, Sigma, 2014 For a finite alphabet ${\mathcal{A}}$ and shift $X\subseteq {\mathcal{A}}^{\mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group $\text{Aut}(X)$.
Van Cyr, Bryna Kra
semanticscholar +1 more source
Open Mathematics, 2020 A Cayley graph Γ\Gamma on a group G is called a dual Cayley graph on G if the left regular representation of G is a subgroup of the automorphism group of Γ\Gamma (note that the right regular representation of G is always an automorphism group of Γ ...
Pan Jiangmin
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