ON FINITENESS CONDITIONS OF CERTAIN GRAPHS OF GROUPS

1995 ◽  
Vol 05 (06) ◽  
pp. 719-724 ◽  
Author(s):  
E. RAPTIS ◽  
OLYMPIA TALELLI ◽  
D. VARSOS
Keyword(s):  
Finiteness Conditions ◽  
Graphs Of Groups

AN EXAMPLE OF A SUBGROUP SEPARABLE BUT NOT CONJUGACY SEPARABLE GROUP

2012 ◽  
Vol 22 (08) ◽  
pp. 1240006 ◽  
Author(s):  
S. C. CHAGAS ◽  
K. S. DE OLIVEIRA ◽  
P. A. ZALESSKII
Keyword(s):  
Finiteness Conditions ◽  
Separable Group ◽  
Graphs Of Groups ◽  
The Third ◽  
Closed Orbits ◽  
Finite Approximability ◽  
Amalgamated Products ◽  
Conjugacy Separable

We give an example of a conjugacy separable, but not subgroup separable group. It is an adaptation of an example of Tavgen and the third author from [Closed orbits and finite approximability with respect to conjugacy of free amalgamated products, Math. Notes58 (1995) 1042–1048] to a theorem of Raptis [On finiteness conditions of certain graphs of groups, Internat. J. Algebra Comput.5 (1995) 719–724].

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros
Keyword(s):  
Fundamental Group ◽  
Koszul Complex ◽  
Finiteness Conditions ◽  
Inverse Systems ◽  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

scholarly journals Graphical splittings of Artin kernels

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Enrique Miguel Barquinero ◽  
Lorenzo Ruffoni ◽  
Kaidi Ye
Keyword(s):  
Free Group ◽  
Artin Group ◽  
Artin Groups ◽  
Graphs Of Groups ◽  
Underlying Graph ◽  
Block Graphs ◽  
Right Angled Artin Groups

Abstract We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is chordal, we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag–Solitar group of variable rank. In particular, for block graphs (e.g. trees), we obtain an explicit rank formula and discuss some features of the space of fibrations of the associated right-angled Artin group.

Finiteness conditions and relative derived categories

2021 ◽  
Vol 573 ◽  
pp. 270-296
Author(s):  
Lingling Tan ◽  
Dingguo Wang ◽  
Tiwei Zhao
Keyword(s):  
Derived Categories ◽  
Finiteness Conditions

scholarly journals A criterion for residual 𝑝-finiteness of arbitrary graphs of finite 𝑝-groups

2019 ◽  
Vol 22 (5) ◽  
pp. 837-844
Author(s):  
Gareth Wilkes
Keyword(s):  
Fundamental Group ◽  
Infinite Graphs ◽  
Graphs Of Groups ◽  
Arbitrary Graphs

Abstract We establish conditions under which the fundamental group of a graph of finite p-groups is necessarily residually p-finite. The technique of proof is independent of previously established results of this type, and the result is also valid for infinite graphs of groups.

scholarly journals Homological finiteness conditions for a class of metabelian groups

2017 ◽  
Vol 50 (1) ◽  
pp. 17-25
Author(s):  
Peter H. Kropholler ◽  
Joseph P. Mullaney
Keyword(s):  
Finiteness Conditions ◽  
Metabelian Groups

scholarly journals INJECTIVE MODULES OVER DOWN-UP ALGEBRAS

2010 ◽  
Vol 52 (A) ◽  
pp. 53-59 ◽  
Author(s):  
PAULA A. A. B. CARVALHO ◽  
CHRISTIAN LOMP ◽  
DILEK PUSAT-YILMAZ
Keyword(s):  
Roots Of Unity ◽  
Finiteness Conditions ◽  
Simple Modules ◽  
Injective Modules ◽  
Injective Hulls

AbstractThe purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.

Subgroups of Finite Index in Free Groups

1949 ◽  
Vol 1 (2) ◽  
pp. 187-190 ◽  
Author(s):  
Marshall Hall
Keyword(s):  
Free Group ◽  
Finite Index ◽  
Free Groups ◽  
Recursion Formula ◽  
Independent Interest ◽  
Finiteness Conditions ◽  
Total Length ◽  
Free Generators

This paper has as its chief aim the establishment of two formulae associated with subgroups of finite index in free groups. The first of these (Theorem 3.1) gives an expression for the total length of the free generators of a subgroup U of the free group Fr with r generators. The second (Theorem 5.2) gives a recursion formula for calculating the number of distinct subgroups of index n in Fr.Of some independent interest are two theorems used which do not involve any finiteness conditions. These are concerned with ways of determining a subgroup U of F.

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