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Howe Duality and Dynamical Weyl Group. [PDF]

Transform Groups
Dalipi R, Felder G, Gurenkova A.
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Decompositions of Hyperbolic Kac-Moody Algebras with Respect to Imaginary Root Groups. [PDF]

Commun Math Phys
Feingold AJ, Kleinschmidt A, Nicolai H.
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NILPOTENCY IN UNCOUNTABLE GROUPS

Journal of the Australian Mathematical Society, 2016
The main purpose of this paper is to investigate the behaviour of uncountable groups of cardinality $\aleph$ in which all proper subgroups of cardinality $\aleph$ are nilpotent. It is proved that such a group $G$ is nilpotent, provided that $G$ has no infinite simple homomorphic images and either $\aleph$ has cofinality strictly larger than $\aleph _{0}
De Giovanni, Francesco, Trombetti, Marco
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Automorphism Groups of Nilpotent Groups

Bulletin of the London Mathematical Society, 1989
Let \({\mathfrak X}\) 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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Nilpotent fuzzy groups

Fuzzy Sets and Systems, 1999
The paper examines families of fuzzy groups [cf. \textit{M. Asaad, S. Abou-Zaid}, Fuzzy Sets Syst. 60, No. 3, 321-323 (1993; Zbl 0814.20061); \textit{J.-G. Kim}, Inf. Sci. 83, No. 3-4, 161-174 (1995; Zbl 0870.20057); \textit{M.~A.~A. Mishref}, J. Fuzzy Math. 6, No. 4, 811-819 (1998; Zbl 0922.20067)].
K. C. Gupta, B. K. Sarma
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A Criterion for a Group to be Nilpotent

Bulletin of the London Mathematical Society, 1992
Let \(G\) be a finite group. The character degree frequency \(m_ G: \mathbb{N} \to \mathbb{Z}\) is defined \(m_ G(n) = |\{\chi \in \text{Irr }G\mid\chi(1) = n\}|\) and the class size frequency function \(w_ G: \mathbb{N} \to \mathbb{Z}\) by \(w_ G(n) = (1/n)|\{g \in G\mid| G: C_ G(g)| = n\}|\) which is the number of conjugacy classes of \(G\) with \(n\)
Cossey, John, Hawkes, Trevor, Mann, Avinoam   +2 more
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Semivarieties of nilpotent groups

Algebra and Logic, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On a Property of Nilpotent Groups

Canadian Mathematical Bulletin, 1994
AbstractLet g be an element of a group G and [g, G] = 〈g-1a-1ga | a ∊ G〉. We prove that if G is locally nilpotent then for each g,t ∊ G either g[g, G] = t[t, G] or g[g, G] ∩ t[t, G] = Ø. The converse is true if G is finite.
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On Constructive Nilpotent Groups

2016
The purpose of this paper to review the results on the constructive nilpotent groups, not claiming to be complete. We consider both the fundamental questions, which are general in the computable algebra, such as the problems of existence, uniqueness, and extension of constructivizations (computable copies), and the questions that arise from the study ...
Nazif G. Khisamiev, Ivan V. Latkin
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On constructive nilpotent groups

Siberian Mathematical Journal, 2007
Summary: We prove the following: (1) a torsion-free class 2 nilpotent group is constructivizable if and only if it is isomorphic to the extension of some constructive Abelian group included in the center of the group by some constructive torsion-free Abelian group and some recursive system of factors; (2) a constructivizable torsion-free class 2 ...
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