Results 271 to 280 of about 1,227,897 (305)

The linearity of automorphism groups of relatively free groups

Mathematical Notes, 1995
Let \({\mathcal N}_c\) be the variety of all nilpotent groups of class \(c\) (\(c\geq 1\)), \(\mathcal U\) be the variety of all abelian groups, \({\mathcal U}_k\) be the variety of all abelian groups of exponent \(k\), \({\mathcal B}_m\) be the variety of all locally finite groups of exponent \(m\) and \(\mathcal I\) be the variety of all groups.
Matejko, O. M., Tavgen', O. I.
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Relatively free products of Magnus groups

Journal of Mathematical Sciences, 2006
A group \(G\) is called a Magnus group if 1) \(\bigcap_{i=1}^\infty\gamma_iG=1\); 2) \(\gamma_iG/\gamma_{i+1}G\) are Abelian torsion free groups. It is shown that the class of Magnus \(\mathfrak{AN}_c\)-groups is closed with respect to \(\mathfrak{AN}_c\)-products.
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Analytic relatively free pro-p groups

Journal of Group Theory, 2004
An absolutely free pro-\(p\) group of rank greater than \(1\) is not \(p\)-adic analytic. In the paper under review it is shown that if a relatively free pro-\(p\) group is \(p\)-adic analytic, then it is topologically finitely generated and nilpotent-by-finite. This confirms a conjecture of A.~Shalev.
Burns, R. G., Medvedev, Yuri
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On the Group of Reduced Identities of Relatively Free Solvable Groups

Siberian Mathematical Journal, 2002
The author uses the basic notions of algebraic geometry over a fixed group \(G\) [see \textit{G. Baumslag}, \textit{A. Myasnikov}, \textit{V. Remeslennikov}, J. Algebra 219, No. 1, 16-79 (1999; Zbl 0938.20020)]. A group \(H\) with fixed embedding \(G\to H\) is called \(G\)-group. Denote the free product \(G*F(X)\) by \(G[X]\).
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ERRATUM: "ON RESTRICTING SUBSETS OF BASES IN RELATIVELY FREE GROUPS"

International Journal of Algebra and Computation, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lucas Sabalka, Dmytro Savchuk
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Free Modules of Relative Invariants of Finite Groups

Studies in Applied Mathematics, 1989
This paper addresses questions about when modules of relative invariants of a finite group G acting on a polynomial ring R are free over the ring of invariant polynomials RG. A converse (first obtained by Shchvartsman) is proven of a result asserting that these modules are always free when the group is generated by pseudoreflections. We also re‐prove
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AUTOMORPHISMS OF CERTAIN RELATIVELY FREE GROUPS AND LIE ALGEBRAS

International Journal of Algebra and Computation, 2004
For positive integers n and c, with n≥2, let Gn,c be a relatively free group of rank n in the variety N2A∧AN2∧Nc. It is shown that there exists an explicitly described finite subset Ω of IA-automorphisms of Gn,c such that the cardinality of Ω is independent upon n and c and the subgroup of the automorphism group Aut (Gn,c) of Gn,c generated by the ...
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Relatively free, nearly nilpotent groups

Mathematical Notes of the Academy of Sciences of the USSR, 1972
We show that a free nilpotent group of countable rank, as well as a free group of countable rank of the variety defined by the identity [[x1 x2,..., xn], [xn+1, xn+2]]=1, satisfies the maximal condition for normal subgroups admitting endomorphisms induced by order preserving one-to-one mappings of the set of free generators into itself.
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ON THE BERGMAN PROPERTY FOR THE AUTOMORPHISM GROUPS OF RELATIVELY FREE GROUPS

Journal of the London Mathematical Society, 2006
A group has the Bergman property. Also, we obtain a partial answer to a question posed by Bergman by establishing that the automorphism group of a free group of countably infinite rank is a group of uniformly finite width.
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The Birkhoff-Neumann embedding of relatively free groups.

2006
Let \(H\) be a finite group, let \(\mathbf V\) be the variety generated by \(H\) and for \(r\geq 1\) let \(G_r\) be the relatively free group in \(\mathbf V\) on \(r\) free generators. Results of \textit{G. Birkhoff} [Proc. Camb. Philos. Soc. 31, 433-454 (1935; Zbl 0013.00105)] and \textit{B. H. Neumann} [Math. Ann. 114, 506-525 (1937; Zbl 0016.35102)]
R. Brandl, G. Corsi Tani, SERENA, LUIGI
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