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 Inverse limits of finite rank free groups

2012 ◽  
Vol 15 (6) ◽  
Author(s):  
Gregory R. Conner ◽  
Curtis Kent
Keyword(s):  
Homomorphic Image ◽  
Free Group ◽  
Finite Rank ◽  
Inverse Limit ◽  
Free Groups ◽  
Inverse System ◽  
Inverse Limits ◽  
Universal Group ◽  
Hawaiian Earring ◽  
Constant System

Abstract.We will show that the inverse limit of finite rank free groups with surjective connecting homomorphism is isomorphic either to a finite rank free group or to a fixed universal group. In other words, any inverse system of finite rank free groups which is not equivalent to an eventually constant system has the universal group as its limit. This universal inverse limit is naturally isomorphic to the first shape group of the Hawaiian earring. We also give an example of a homomorphic image of the Hawaiian earring group which lies in the inverse limit of free groups but is neither a free group nor isomorphic to the Hawaiian earring group.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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.

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 A characterization of a map whose inverse limit is an arc

2021 ◽  
pp. 1-17
Author(s):  
SINA GREENWOOD ◽  
SONJA ŠTIMAC
Keyword(s):  
Continuous Function ◽  
Inverse Limit ◽  
Splitting Sequence

Abstract For a continuous function $f:[0,1] \to [0,1]$ we define a splitting sequence admitted by f and show that the inverse limit of f is an arc if and only if f does not admit a splitting sequence.

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
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