scholarly journals THE ORE CONDITION, AFFILIATED OPERATORS, AND THE LAMPLIGHTER GROUP

2003 ◽  
Author(s):  
PETER A. LINNELL ◽  
WOLFGANG LÜCK ◽  
THOMAS SCHICK
Keyword(s):  
Lamplighter Group ◽  
Ore Condition

Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups

2021 ◽  
pp. 1-36
Author(s):  
ARIE LEVIT ◽  
ALEXANDER LUBOTZKY
Keyword(s):  
Ergodic Theorem ◽  
Abelian Groups ◽  
Wreath Products ◽  
Finitely Generated ◽  
Metabelian Groups ◽  
Amenable Groups ◽  
Pointwise Ergodic Theorem ◽  
Lamplighter Group ◽  
Invariant Random Subgroups

Abstract We prove that all invariant random subgroups of the lamplighter group L are co-sofic. It follows that L is permutation stable, providing an example of an infinitely presented such group. Our proof applies more generally to all permutational wreath products of finitely generated abelian groups. We rely on the pointwise ergodic theorem for amenable groups.

The Lamplighter Group L2

2018 ◽  
pp. 105-132
Author(s):  
Marianna C. Bonanome ◽  
Margaret H. Dean ◽  
Judith Putnam Dean
Keyword(s):  
Lamplighter Group

On the Ring of Quotients at a Prime Ideal of a Right Noetherian Ring

1972 ◽  
Vol 24 (4) ◽  
pp. 703-712 ◽  
Author(s):  
A. G. Heinicke
Keyword(s):  
Prime Ideal ◽  
Noetherian Ring ◽  
Quotient Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Torsion Class ◽  
Ring Of Quotients ◽  
Ore Condition ◽  
The Right ◽  
Necessary And Sufficient

J. Lambek and G. Michler [3] have initiated the study of a ring of quotients RP associated with a two-sided prime ideal P in a right noetherian ring R. The ring RP is the quotient ring (in the sense of [1]) associated with the hereditary torsion class τ consisting of all right R-modules M for which HomR(M, ER(R/P)) = 0, where ER(X) is the injective hull of the R-module X.In the present paper, we shall study further the properties of the ring RP. The main results are Theorems 4.3 and 4.6. Theorem 4.3 gives necessary and sufficient conditions for the torsion class associated with P to have property (T), as well as some properties of RP when these conditions are indeed satisfied, while Theorem 4.6 gives necessary and sufficient conditions for R to satisfy the right Ore condition with respect to (P).

scholarly journals Ore-condition and Z3-connectivity

2008 ◽  
Vol 29 (7) ◽  
pp. 1587-1595 ◽  
Author(s):  
Rong Luo ◽  
Rui Xu ◽  
Jianhua Yin ◽  
Gexin Yu
Keyword(s):  
Ore Condition

Some limits related to random iterations of a lamplighter group

2008 ◽  
Vol 78 (1) ◽  
pp. 21-26
Author(s):  
Luis G. Gorostiza ◽  
Martha Takane
Keyword(s):  
Lamplighter Group

scholarly journals Law of large numbers for the drift of the two-dimensional wreath product

2021 ◽  
Author(s):  
Anna Erschler ◽  
Tianyi Zheng
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Wreath Product ◽  
Law Of Large Numbers ◽  
Abelian Groups ◽  
Limiting Distribution ◽  
Two Dimensional ◽  
Lamplighter Group ◽  
Large Numbers ◽  
Asymptotic Geometry

AbstractWe prove the law of large numbers for the drift of random walks on the two-dimensional lamplighter group, under the assumption that the random walk has finite $$(2+\epsilon )$$ ( 2 + ϵ ) -moment. This result is in contrast with classical examples of abelian groups, where the displacement after n steps, normalised by its mean, does not concentrate, and the limiting distribution of the normalised n-step displacement admits a density whose support is $$[0,\infty )$$ [ 0 , ∞ ) . We study further examples of groups, some with random walks satisfying LLN for drift and other examples where such concentration phenomenon does not hold, and study relation of this property with asymptotic geometry of groups.

scholarly journals The Conjugacy Ratio of Groups

2019 ◽  
Vol 62 (3) ◽  
pp. 895-911 ◽  
Author(s):  
Laura Ciobanu ◽  
Charles Garnet Cox ◽  
Armando Martino
Keyword(s):  
Finite Groups ◽  
Hyperbolic Groups ◽  
Finitely Generated ◽  
Residually Finite ◽  
Subexponential Growth ◽  
Finitely Generated Group ◽  
Growth Functions ◽  
Lamplighter Group ◽  
Residually Finite Groups ◽  
Right Angled Artin Groups

AbstractIn this paper we introduce and study the conjugacy ratio of a finitely generated group, which is the limit at infinity of the quotient of the conjugacy and standard growth functions. We conjecture that the conjugacy ratio is 0 for all groups except the virtually abelian ones, and confirm this conjecture for certain residually finite groups of subexponential growth, hyperbolic groups, right-angled Artin groups and the lamplighter group.

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