scholarly journals A subgroup theorem for homological filling functions

2016 ◽  
Vol 10 (3) ◽  
pp. 867-883 ◽  
Author(s):  
Richard Gaelan Hanlon ◽  
Eduardo Martínez Pedroza
Keyword(s):  
Subgroup Theorem

scholarly journals A note on free products with a normal amalgamation

1968 ◽  
Vol 8 (3) ◽  
pp. 631-637 ◽  
Author(s):  
R. A. Bryce
Keyword(s):  
Free Products ◽  
One To One ◽  
Image Position ◽  
Subgroup Theorem ◽  
Infinite Cycles

It is a consequence of the Kurosh subgroup theorem for free products that if a group has two decompositions where each Ai and each Bj is indecomposable, then I and J can be placed in one-to-one correspondence so that corresponding groups if not conjugate are infinite cycles. We prove here a corresponding result for free products with a normal amalgamation.

FREE INVERSE MONOIDS AND GRAPH IMMERSIONS

1993 ◽  
Vol 03 (01) ◽  
pp. 79-99 ◽  
Author(s):  
STUART W. MARGOLIS ◽  
JOHN C. MEAKIN
Keyword(s):  
Formal Language ◽  
Inverse Monoid ◽  
Finitely Generated ◽  
Inverse Monoids ◽  
Rational Subset ◽  
The Relationship ◽  
Subgroup Theorem ◽  
Free Inverse Monoid ◽  
Natural Way

The relationship between covering spaces of graphs and subgroups of the free group leads to a rapid proof of the Nielsen-Schreier subgroup theorem. We show here that a similar relationship holds between immersions of graphs and closed inverse submonoids of free inverse monoids. We prove using these methods, that a closed inverse submonoid of a free inverse monoid is finitely generated if and only if it has finite index if and only if it is a rational subset of the free inverse monoid in the sense of formal language theory. We solve the word problem for the free inverse category over a graph Γ. We show that immersions over Γ may be classified via conjugacy classes of loop monoids of the free inverse category over Γ. In the case that Γ is a bouquet of X circles, we prove that the category of (connected) immersions over Γ is equivalent to the category of (transitive) representations of the free inverse monoid FIM(X). Such representations are coded by closed inverse submonoids of FIM(X). These monoids will be constructed in a natural way from groups acting freely on trees and they admit an idempotent pure retract onto a free inverse monoid. Applications to the classification of finitely generated subgroups of free groups via finite inverse monoids are developed.

scholarly journals Solvable Subgroup Theorem for simplicial nonpositive curvature

2018 ◽  
Vol 28 (04) ◽  
pp. 605-611
Author(s):  
Tomasz Prytuła
Keyword(s):  
Nonpositive Curvature ◽  
Decomposition Theorem ◽  
Solvable Subgroup ◽  
Finitely Generated ◽  
Flat Torus ◽  
Product Decomposition ◽  
Subgroup Theorem

Given a group [Formula: see text] with bounded torsion that acts properly on a systolic complex, we show that every solvable subgroup of [Formula: see text] is finitely generated and virtually abelian of rank at most [Formula: see text]. In particular, this gives a new proof of the above theorem for systolic groups. The main tools used in the proof are the Product Decomposition Theorem and the Flat Torus Theorem.

scholarly journals A focal subgroup theorem for outer commutator words

2012 ◽  
Vol 15 (3) ◽  
Author(s):  
Cristina Acciarri ◽  
Gustavo A. Fernández-Alcober ◽  
Pavel Shumyatsky
Keyword(s):  
Outer Commutator ◽  
Subgroup Theorem

Abstract.Let

scholarly journals Subgroup theorem for valuated groups and the CSA property

2010 ◽  
Vol 324 (2) ◽  
pp. 159-182
Author(s):  
Abderezak Ould Houcine
Keyword(s):  
Subgroup Theorem
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