Some properties of a magnus embedding

1970 ◽  
Vol 9 (5) ◽  
pp. 342-349 ◽  
Author(s):  
V. N. Remeslennikov ◽  
V. G. Sokolov
Keyword(s):  
Magnus Embedding

A remark on spherical equations in free metabelian groups

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Evgeny I. Timoshenko
Keyword(s):  
Metabelian Groups ◽  
Diophantine Problem ◽  
Magnus Embedding

AbstractI. Lysenok and A. Ushakov proved that the Diophantine problem for spherical quadric equations in free metabelian groups is solvable. The present paper proves this result by using the Magnus embedding.

scholarly journals On the Magnus–Smelkin embedding

1987 ◽  
Vol 30 (1) ◽  
pp. 133-142
Author(s):  
J. Mccool∗
Keyword(s):  
Normal Subgroup ◽  
Free Group ◽  
Semidirect Product ◽  
Generating Set ◽  
Variety Of Groups ◽  
Magnus Embedding

The generalization of the Magnus embedding [7] proved by Smelkin [9] may bestated as follows. Let L be a free group freely generated by the set xi(i∈I), and let R be a normal subgroup of L with G = L/R. If V is any variety of groups and ∏ is the V-freegroup with free generating set the symbols [g, xi] (g∈G, i∈I), then L/V(R) is embeddedin the semidirect product ∏ ⋊ G (where the action of G on ∏ is given by h · [g, xi] = [hg, xi], for h, g ∈ G).

scholarly journals Metric behaviour of the Magnus embedding

2014 ◽  
Vol 176 (1) ◽  
pp. 305-313
Author(s):  
Andrew W. Sale
Keyword(s):  
Magnus Embedding

scholarly journals THE MAGNUS EMBEDDING IS A QUASI-ISOMETRY

2012 ◽  
Vol 22 (08) ◽  
pp. 1240005
Author(s):  
SVETLA VASSILEVA
Keyword(s):  
Wreath Product ◽  
Solvable Group ◽  
Free Solvable Group ◽  
Magnus Embedding

We show that the Magnus embedding, which embeds the free solvable group Sd, r of rank r and degree d into the wreath product ℤr ≀ Sd-1, r, is a quasi-isometry.

The Magnus Embedding

1969 ◽  
Vol s1-44 (1) ◽  
pp. 115-117 ◽  
Author(s):  
M. J. Dunwoody
Keyword(s):  
Magnus Embedding

scholarly journals Parallel identity testing for skew circuits with big powers and applications

2018 ◽  
Vol 28 (06) ◽  
pp. 979-1004 ◽  
Author(s):  
Daniel König ◽  
Markus Lohrey
Keyword(s):  
Word Problem ◽  
Metabelian Group ◽  
Wreath Products ◽  
Arithmetic Circuits ◽  
Identity Testing ◽  
Straight Line ◽  
Higher Dimensional ◽  
Magnus Embedding ◽  
The One ◽  
Straight Line Programs

Powerful skew arithmetic circuits are introduced. These are skew arithmetic circuits with variables, where input gates can be labeled with powers [Formula: see text] for binary encoded numbers [Formula: see text]. It is shown that polynomial identity testing for powerful skew arithmetic circuits belongs to [Formula: see text], which generalizes a corresponding result for (standard) skew circuits. Two applications of this result are presented: (i) Equivalence of higher-dimensional straight-line programs can be tested in [Formula: see text]; this result is even new in the one-dimensional case, where the straight-line programs produce words. (ii) The compressed word problem (or circuit evaluation problem) for certain wreath products of finitely generated abelian groups belongs to [Formula: see text]. Using the Magnus embedding, it follows that the compressed word problem for a free metabelian group belongs to [Formula: see text].

The Magnus Embedding for Right-Symmetric Algebras

2004 ◽  
Vol 45 (3) ◽  
pp. 488-494 ◽  
Author(s):  
D. Kh. Kozybaev ◽  
U. U. Umirbaev
Keyword(s):  
Symmetric Algebras ◽  
Magnus Embedding

scholarly journals Magnus embedding and algorithmic properties of groups $F/N^{(d)}$

2016 ◽  
Vol 369 (9) ◽  
pp. 6189-6206 ◽  
Author(s):  
Funda Gul ◽  
Mahmood Sohrabi ◽  
Alexander Ushakov
Keyword(s):  
Magnus Embedding
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