scholarly journals On the finite presentation of subdirect products and the nature of residually free groups

2013 ◽  
Vol 135 (4) ◽  
pp. 891-933 ◽  
Author(s):  
Martin R. Bridson ◽  
James Howie ◽  
Charles F. Miller ◽  
Hamish Short
Keyword(s):  
Free Groups ◽  
Finite Presentation ◽  
Subdirect Products

scholarly journals STAR-FREE GEODESIC LANGUAGES FOR GROUPS

2007 ◽  
Vol 17 (02) ◽  
pp. 329-345 ◽  
Author(s):  
SUSAN HERMILLER ◽  
DEREK F. HOLT ◽  
SARAH REES
Keyword(s):  
Regular Language ◽  
Abelian Groups ◽  
Free Groups ◽  
Direct Products ◽  
Small Cancellation ◽  
Generating Set ◽  
Finite Presentation

In this article we show that every group with a finite presentation satisfying one or both of the small cancellation conditions C′(1/6) and C′(1/4) - T(4) has the property that the set of all geodesics (over the same generating set) is a star-free regular language. Star-free regularity of the geodesic set is shown to be dependent on the generating set chosen, even for free groups. We also show that the class of groups whose geodesic sets are star-free with respect to some generating set is closed under taking graph (and hence free and direct) products, and includes all virtually abelian groups.

scholarly journals Discriminantal bundles, arrangement groups, and subdirect products of free groups

2020 ◽  
Vol 6 (3) ◽  
pp. 751-789 ◽  
Author(s):  
Daniel C. Cohen ◽  
Michael J. Falk ◽  
Richard C. Randell
Keyword(s):  
Free Groups ◽  
Subdirect Products

Subgroups of products of surface groups

1999 ◽  
Vol 126 (2) ◽  
pp. 195-208 ◽  
Author(s):  
F. E. A. JOHNSON
Keyword(s):  
Direct Product ◽  
Free Groups ◽  
Orientable Surface ◽  
Fuchsian Groups ◽  
Surface Groups ◽  
Finitely Generated ◽  
Isomorphism Classes ◽  
Relative Invariant ◽  
Finiteness Result ◽  
Subdirect Products

The subgroup structure of a direct product of two Fuchsian groups is very complicated; for example, Baumslag and Roseblade [1] have shown that a direct product Fm1×Fm2 of finitely generated free groups contains continuously many distinct isomorphism classes of finitely generated subgroups. The situation is much simpler, however, if attention is restricted to finitely generated normal subgroups of Fm1×Fm2; then on general grounds one cannot expect to get more than a countable infinity, but, in fact, the situation is almost finite; we showed, in [4], that Fm1×Fm2 contains precisely 1+min{m1, m2} orbits of maximal normal subdirect products under the natural action of its automorphism group.In this paper we study the situation which arises if the free groups Fmi are replaced by fundamental groups of closed surfaces. This question was previously considered by Nigel Carr in the final chapter of his (unpublished) thesis [2]. By appealing to the relative invariant theory of pairs of skew bilinear forms, Carr was able to show that in a direct product Σg1×Σg2 of orientable surface groups of genus [ges ]2 the number of orbits of maximal normal subdirect products is always infinite. Here we refine and extend Carr's approach to study the manner in which the finiteness result of [4] breaks down on passing to more general Fuchsian groups.

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 Kähler groups and subdirect products of surface groups

2020 ◽  
Vol 24 (2) ◽  
pp. 971-1017
Author(s):  
Claudio Llosa Isenrich
Keyword(s):  
Surface Groups ◽  
Kähler Groups ◽  
Subdirect Products

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 On the lattice of varieties of completely regular semigroups

1983 ◽  
Vol 35 (2) ◽  
pp. 227-235 ◽  
Author(s):  
P. R. Jones
Keyword(s):  
Lattice Of Varieties ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Variety Of Groups ◽  
Completely Regular Semigroups ◽  
Subdirect Products

AbstractSeveral morphisms of this lattice V(CR) are found, leading to decompostions of it, and various sublattices, into subdirect products of interval sublattices. For example the map V → V ∪ G (where G is the variety of groups) is shown to be a retraction of V(CR); from modularity of the lattice V(BG) of varieties of bands of groups it follows that the map V → (V ∪ V V G) is an isomorphism of V(BG).

scholarly journals Products of free groups in Lie groups

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