Results 31 to 40 of about 7,845,575 (284)
Hodge-Deligne polynomials of character varieties of free abelian groups
Open Mathematics, 2021 Let FF be a finite group and XX be a complex quasi-projective FF-variety. For r∈Nr\in {\mathbb{N}}, we consider the mixed Hodge-Deligne polynomials of quotients Xr/F{X}^{r}\hspace{-0.15em}\text{/}\hspace{-0.08em}F, where FF acts diagonally, and compute ...
Florentino Carlos, Silva Jaime
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Finitely generated subgroups of free groups as formal languages and their cogrowth [PDF]
Groups, Complexity, Cryptology, 2021 For finitely generated subgroups $H$ of a free group $F_m$ of finite rank $m$, we study the language $L_H$ of reduced words that represent $H$ which is a regular language.
Arman Darbinyan +2 more
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Scale-Free Dynamics in Animal Groups and Brain Networks
Frontiers in Systems Neuroscience, 2021 Collective phenomena fascinate by the emergence of order in systems composed of a myriad of small entities. They are ubiquitous in nature and can be found over a vast range of scales in physical and biological systems.
Tiago L. Ribeiro +3 more
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On the Geometry of the Automorphism Group of a Free Group
Bulletin of the London Mathematical Society, 1995 The groups \(\Aut(F_3)\) and \(\text{Out}(F_3)\) satisfy strictly exponential isoperimetric inequalities; in particular, they are not automatic. For \(n\geq 3\), \(\Aut(F_n)\) and \(\text{Out}(F_n)\) do not admit bounded bicombings of sub-exponential length, hence they cannot act properly and cocompactly by isometries of any simply-connected space of ...
Bridson, M, Vogtmann, K
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Nagoya Mathematical Journal, 1954 The purpose of this note is to prove the following proposition, which is made use of in the preceding paper by Mr. M. Kuranishi in this number. First we shall explain the notations. Let be a word with respect to two letters, and let G be a free group generated by two free generators x and y.
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Homogeneity in the free group [PDF]
Duke Mathematical Journal, 2012 26 ...
Perin, Chloé, Sklinos, Rizos
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Unitary representability of free abelian topological groups
Applied General Topology, 2008 For every Tikhonov space X the free abelian topological group A(X) and the free locally convex vector space L(X) admit a topologically faithful unitary representation. For compact spaces X this is due to Jorge Galindo.
Vladimir V. Uspenskij
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The character of free topological groups I
Applied General Topology, 2005 A systematic analysis is made of the character of the free and free abelian topological groups on uniform spaces and on topological spaces. In the case of the free abelian topological group on a uniform space, expressions are given for the character in ...
Peter Nickolas, Mikhail Tkachenko
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Commutators and Squares in Free Nilpotent Groups
International Journal of Mathematics and Mathematical Sciences, 2009 In a free group no nontrivial commutator is a square. And in the free group F2=F(x1,x2) freely generated by x1,x2 the commutator [x1,x2] is never the product of two squares in F2, although it is always the product of three squares.
Mehri Akhavan-Malayeri
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On the automorphism groups of relatively free groups of infinite rank: a survey
Қарағанды университетінің хабаршысы. Математика сериясы, 2018 The paper is intended to be a survey on some topics within the framework of automorphisms of a relatively free groups of infinite rank. We discuss such properties as tameness, primitivity, small index, Bergman property, and so on.
V.A. Roman’kov
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