Free groups and the amenability of Lie groups

1988 ◽  
pp. 95-123 ◽  
Author(s):  
Alan Paterson
Keyword(s):  
Lie Groups ◽  
Free Groups

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 Everywhere Dense Imbedding of Free Groups in Lie Groups

1951 ◽  
Vol 2 ◽  
pp. 63-71 ◽  
Author(s):  
Masatake Kuranishi
Keyword(s):  
Lie Groups ◽  
Free Group ◽  
Free Groups ◽  
Dense Subgroup ◽  
Discrete Subgroups ◽  
Simple Lie Groups

In this note it will be proved that some kinds of Lie groups (including semi-simple Lie groups) have an everywhere dense subgroup which is algebraically isomorphic to the free group generated by two elements (Theorem 8),In § 1 characterizations of Lie groups which are approximated by discrete subgroups’ are given. This section is closely connected with a part of the results of Malcev [4] and Matsushima [5], and some theorems are slight modifications of them (Theorems 2 and 3).

scholarly journals Deficiencies of lattices in connected Lie groups

2002 ◽  
Vol 65 (3) ◽  
pp. 393-397 ◽  
Author(s):  
Jonathan A. Hillman
Keyword(s):  
Lie Groups ◽  
Free Groups ◽  
Torsion Free

We complete the determination of the groups of positive deficiency which occur as lattices in connected Lie groups. The torsion free groups among them are 3-mainfold groups. We show that any other torsion free 3-manifold group which is such a lattice is the group of an aspherical closed geometric 3-manifold.

scholarly journals ENGEL RELATIONS IN 4-MANIFOLD TOPOLOGY

2016 ◽  
Vol 4 ◽  
Author(s):  
MICHAEL FREEDMAN ◽  
VYACHESLAV KRUSHKAL
Keyword(s):  
Lie Groups ◽  
Free Groups ◽  
Higher Order ◽  
Double Points

We give two applications of the 2-Engel relation, classically studied in finite and Lie groups, to the 4-dimensional (4D) topological surgery conjecture. The A–B slice problem, a reformulation of the surgery conjecture for free groups, is shown to admit a homotopy solution. We also exhibit a new collection of universal surgery problems, defined using ramifications of homotopically trivial links. More generally we show how $n$-Engel relations arise from higher-order double points of surfaces in 4-space.

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.

Sign in / Sign up

Export Citation Format

Share Document