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Peano's Infinite Mirrors: Automorphism Groups of Non-Standard Models
This paper explores the intricate structure of automorphism groups of non-standard models of Peano Arithmetic (PA), conceptualizing them as "Peano's Infinite Mirrors". Non-standard models, rich and complex structures extending the natural numbers, possess symmetries that are often far more elaborate than those found in the standard model. We delve into
SÉRGIO DE ANDRADE, PAULO
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Automorphisms of Mackey groups
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, 2023 We consider total subspaces of linear functionals on an infinite-dimensional vector space and the related Mackey algebras and groups. We outline the description of automorphisms of Mackey groups SL∞(V|W), O∞(f), and SU∞(f) over fields of characteristics ...
O. Bezushchak
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On automorphisms and splittings of special groups [PDF]
Compositio Mathematica, 2021 We initiate the study of outer automorphism groups of special groups $G$, in the Haglund–Wise sense. We show that $\operatorname {Out}(G)$ is infinite if and only if $G$ splits over a co-abelian subgroup of a centraliser and there exists an infinite ...
Elia Fioravanti
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Structure and automorphisms of pure virtual twin groups [PDF]
Monatshefte für Mathematik (Print), 2020 The study of stable isotopy classes of a finite collection of immersed circles without triple or higher intersections on closed oriented surfaces is considered as a planar analogue of virtual knot theory, a far reaching generalisation of classical knot ...
Tushar Kanta Naik +2 more
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From mapping class groups to automorphism groups of free groups [PDF]
, 2005 We show that the natural map from the mapping class groups of surfaces to the automorphism groups of free groups, induces an infinite loop map on the classifying spaces of the stable groups after plus construction.
Wahl, Nathalie
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Generalized spin Sutherland systems revisited
Nuclear Physics B, 2015 We present generalizations of the spin Sutherland systems obtained earlier by Blom and Langmann and by Polychronakos in two different ways: from SU(n) Yang–Mills theory on the cylinder and by constraining geodesic motion on the N-fold direct product of ...
L. Fehér, B.G. Pusztai
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On the Root-class Residuality of HNN-extensions of Groups
Моделирование и анализ информационных систем, 2014 Let K be an arbitrary root class of groups. This means that K contains at least one non-unit group, is closed under taking subgroups and direct products of a finite number of factors and satisfies the Gruenberg condition: if 1 ≤ Z ≤ Y ≤ X is a subnormal ...
E. A. Tumanova
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Braid groups of imprimitive complex reflection groups [PDF]
, 2015 We obtain new presentations for the imprimitive complex reflection groups of type $(de,e,r)$ and their braid groups $B(de,e,r)$ for $d,r \ge 2$. Diagrams for these presentations are proposed.
Corran, Ruth +2 more
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Automorphisms of the loop and arc graph of an infinite-type surface [PDF]
Proceedings of the American Mathematical Society, Series B, 2019 We show that the extended based mapping class group of an infinite-type surface is naturally isomorphic to the automorphism group of the loop graph of that surface.
Anschel Schaffer-Cohen
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On automorphism groups of Toeplitz subshifts
Discrete Analysis, 2017 On automorphism groups of Toeplitz subshifts, Discrete Analysis 2017:11, 19 pp. A discrete dynamical system is a space $X$ with some kind of structure, together with a map $\sigma\colon X\to X$ that preserves the structure.
Sebastian Donoso +3 more
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