scholarly journals Displacements of automorphsism of free groups I: Displacement functions, minpoints and train tracks

2020 ◽  
pp. 1
Author(s):  
Stefano Francaviglia ◽  
Armando Martino
Keyword(s):  
Free Groups ◽  
Train Tracks

Train Tracks and Automorphisms of Free Groups

1992 ◽  
Vol 135 (1) ◽  
pp. 1 ◽  
Author(s):  
Mladen Bestvina ◽  
Michael Handel
Keyword(s):  
Free Groups ◽  
Automorphisms Of Free Groups ◽  
Train Tracks

Automorphisms of Free Groups

2017 ◽  
Author(s):  
Matt Clay
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Symmetric Group ◽  
Cayley Graph ◽  
Free Group ◽  
Free Groups ◽  
Research Projects ◽  
Frobenius Theorem ◽  
Automorphisms Of Free Groups ◽  
Train Tracks

This chapter discusses the automorphisms of free groups. Every group is the collection of symmetries of some object, namely, its Cayley graph. A symmetry of a group is called an automorphism; it is merely an isomorphism of the group to itself. The collection of all of the automorphisms is also a group too, known as the automorphism group and denoted by Aut (G). The chapter considers basic examples of groups to illustrate what an automorphism is, with a focus on the automorphisms of the symmetric group on three elements and of the free abelian group. It also examines the dynamics of an automorphism of a free group and concludes with a description of train tracks, a topological model for the free group, and the Perron–Frobenius theorem. Exercises and research projects are included.

Sulphoamidic Phtalocyaninic Pigments and Dyes(II)

2008 ◽  
Vol 59 (5) ◽  
Author(s):  
Elena Stingaciu ◽  
Corneliu Minca ◽  
Ion Sebe
Keyword(s):  
Ir Spectra ◽  
Aromatic Amines ◽  
Free Groups ◽  
Cyanuric Chloride ◽  
Layer Chromatography ◽  
Phenylene Diamine

This work concerns the synthesis of pigments and phtalocyanine dyes obtained through the sulphonation of copper phtalocyanine and amidation with some aliphatic and aromatic amines (lauryl-amine, i-propyl-amine, hexadecyl-amine, stearyl-amine and acetyl-p-phenylene-diamine) with good properties for the electrotechnic utilisation and for toner materials. The pigments with amino free groups are transformed by condensation with cyanuric chloride in phtalocyanine pigments with different tinctorial properties. The dyes were analyzed through the layer chromatography and were characterized on the IR spectra bases and tinctorial tests.

Generating the inverse limit of free groups

2021 ◽  
Vol 578 ◽  
pp. 371-401
Author(s):  
Gregory R. Conner ◽  
Wolfgang Herfort ◽  
Curtis A. Kent ◽  
Petar Pavešić
Keyword(s):  
Inverse Limit ◽  
Free Groups

scholarly journals Minimal partition-free groups

2021 ◽  
Author(s):  
Afsane Bahri ◽  
Zeinab Akhlaghi ◽  
Behrooz Khosravi
Keyword(s):  
Free Groups

scholarly journals Freely indecomposable almost free groups with free abelianization

2020 ◽  
Vol 23 (3) ◽  
pp. 531-543
Author(s):  
Samuel M. Corson
Keyword(s):  
Free Groups ◽  
Uncountable Cardinals

AbstractFor certain uncountable cardinals κ, we produce a group of cardinality κ which is freely indecomposable, strongly κ-free, and whose abelianization is free abelian of rank κ. The construction takes place in Gödel’s constructible universe L. This strengthens an earlier result of Eklof and Mekler.

scholarly journals Products of free groups in Lie groups

2021 ◽  
Author(s):  
Caterina Campagnolo ◽  
Holger Kammeyer
Keyword(s):  
Lie Groups ◽  
Free Groups

scholarly journals On the structure of some contranormal-free groups

2021 ◽  
pp. 1-7
Author(s):  
Martyn R. Dixon ◽  
Leonid A. Kurdachenko ◽  
Igor Ya. Subbotin
Keyword(s):  
Free Groups

scholarly journals On the graded quotients of the rings of Fricke characters of free groups

2015 ◽  
Vol 430 ◽  
pp. 94-118 ◽  
Author(s):  
Eri Hatakenaka ◽  
Takao Satoh
Keyword(s):  
Free Groups
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