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Adversarial dynamical systems characterize when data-driven learning succeeds or fails. [PDF]

Nat Commun
Colbrook MJ, Mezić I, Stepanenko A.
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INVOLUTIONS IN LOCALLY FINITE GROUPS

Journal of the London Mathematical Society, 2004
Summary: The paper deals with locally finite groups \(G\) having an involution \(\varphi\) such that \(C_G(\varphi)\) is of finite rank. The following theorem gives a very detailed description of such groups. Let \(G\) be a locally finite group having an involution \(\varphi\) such that \(C_G(\varphi)\) is of finite rank.
Kuzucuoğlu, Mahmut, Shumyatsky, Pavel
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Locally Finite Groups

, 1973
Includes bibliographical references (pages 193-208).Print version record.Electronic reproduction.Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1.
Kegel, Otto H., Wehrfritz, Bertram A. F.
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Localization and finite simple groups

Israel Journal of Mathematics, 2006
Let \(H\) and \(G\) be groups. A group homomorphism from \(H\) to \(G\) is called a localization if and only if it induces a bijection between \(\Hom(G,G)\) and \(\Hom(H,G)\). Following \textit{J. L. Rodríguez, J. Scherer} and \textit{J. Thévenaz} [Isr. J. Math.
Parker, Chris, Saxl, Jan
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On Infinite Locally Finite Groups

Canadian Mathematical Bulletin, 1994
AbstractIf G is a group such that every infinite subset of G contains a commuting pair of elements then G is centre-by-finite. This result is due to B. H. Neumann. From this it can be shown that if G is infinite and such that for every pair X, Y of infinite subsets of G there is some x in X and some y in Y that commute, then G is abelian. It is natural
Rhemtulla, Akbar, Smith, Howard
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On local categories of finite groups

Mathematische Zeitschrift, 2011
Let \(\mathcal P\) be a partially ordered set and let \(G\) be a group. Then \(\mathcal P\) is a \(G\)-poset if there is a group homomorphism \(G\to\Aut(\mathcal P)\) giving an action of \(G\) on \(\mathcal P\). The transporter category \(G\propto\mathcal P\) has the same objects as \(\mathcal P\) and morphisms from \(x\) to \(y\) are couples \((g,gx ...
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σ-Subnormality in locally finite groups

Journal of Algebra, 2023
Let \(\sigma=\{\sigma_{j} \mid j \in J\}\) be a partition of the set of prime numbers. A subgroup \(X\) of a finite group \(G\) is \(\sigma\)-subnormal if there exists a chain of subgroups \(X=X_{0} \leq X_{1} \leq \dots \leq X_{n}=G\) such that, for each \(1 \leq i \leq n\), \(X_{i-1} \trianglelefteq X_{i}\) or \(X_{i}/(X_{i-1})_{X_{i}}\) is a ...
Ferrara M., Trombetti M.
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Locally Finite Representations of Polycyclic-by-Finite Groups

Proceedings of the London Mathematical Society, 1982
From the introduction: ``Let \(G\) be a polycyclic-by-finite group, \(k\) a field, and \(V\) a right \(kG\)-module of finite \(k\)-dimension. This work was motivated by Musson's result [in I. M. Musson, Q. J. Math., Oxf. II. Ser. 31, 429--448 (1980; Zbl 0413.16012)], that if \(k\) has positive characteristic then the injective hull \(E(V)\) of \(V\) is
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Locally Finite Simple Groups

1974
The group G is locally finite if each of its finitely generated subgroups is finite. Until rather recently the area of locally finite groups entirely belonged to the wilderness of counter-examples; and there absurdly wild behaviour is possible, indeed. What little progress has been made in cultivating some fringes of this wilderness is essentially due ...
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On the p-Local Rank of Finite Groups

Acta Mathematica Sinica, English Series, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Baoshan, Zhang, Jiping
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