scholarly journals On varieties of groups generated by wreath products of abelian groups

2001 ◽  
pp. 223-238 ◽  
Author(s):  
Vahagn H. Mikaelian
Keyword(s):  
Abelian Groups ◽  
Wreath Products

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.

On the Morava K-theory of some finite 2-groups

1997 ◽  
Vol 121 (1) ◽  
pp. 7-13 ◽  
Author(s):  
BJÖRN SCHUSTER
Keyword(s):  
Finite Group ◽  
Sylow Subgroup ◽  
Cyclic Subgroup ◽  
Abelian Groups ◽  
Wreath Products ◽  
Classifying Space ◽  
Generalized Cohomology ◽  
K Theory ◽  
A Finite Group ◽  
Generalized Quaternion

For any fixed prime p and any non-negative integer n there is a 2(pn − 1)-periodic generalized cohomology theory K(n)*, the nth Morava K-theory. Let G be a finite group and BG its classifying space. For some time now it has been conjectured that K(n)*(BG) is concentrated in even dimensions. Standard transfer arguments show that a finite group enjoys this property whenever its p-Sylow subgroup does, so one is reduced to verifying the conjecture for p-groups. It is easy to see that it holds for abelian groups, and it has been proved for some non-abelian groups as well, namely groups of order p3 ([7]) and certain wreath products ([3], [2]). In this note we consider finite (non-abelian) 2-groups with maximal normal cyclic subgroup, i.e. dihedral, semidihedral, quasidihedral and generalized quaternion groups of order a power of two.

On Coleman automorphisms of wreath products of finite nilpotent groups by abelian groups

2011 ◽  
Vol 54 (10) ◽  
pp. 2253-2257 ◽  
Author(s):  
JinKe Hai ◽  
ZhengXing Li
Keyword(s):  
Abelian Groups ◽  
Nilpotent Groups ◽  
Wreath Products

scholarly journals Metabelian varieties of groups and wreath products of abelian groups

2007 ◽  
Vol 313 (2) ◽  
pp. 455-485 ◽  
Author(s):  
Vahagn H. Mikaelian
Keyword(s):  
Abelian Groups ◽  
Wreath Products

Coleman automorphisms of standard wreath products of finite abelian groups by 2-closed groups

2013 ◽  
Vol 82 (3-4) ◽  
pp. 599-605 ◽  
Author(s):  
ZHENGXING LI ◽  
JINKE HAI
Keyword(s):  
Abelian Groups ◽  
Wreath Products ◽  
Finite Abelian Groups ◽  
Closed Groups

Varieties Generated by Wreath Products of Abelian Groups

2013 ◽  
Vol 195 (4) ◽  
pp. 523-528 ◽  
Author(s):  
V. H. Mikaelian
Keyword(s):  
Abelian Groups ◽  
Wreath Products

The rank and generating set for inverse limits of wreath products of Abelian groups

2012 ◽  
Vol 99 (6) ◽  
pp. 557-565 ◽  
Author(s):  
Adam Woryna
Keyword(s):  
Abelian Groups ◽  
Wreath Products ◽  
Inverse Limits ◽  
Generating Set

Central series in wreath products

1967 ◽  
Vol 63 (3) ◽  
pp. 551-567 ◽  
Author(s):  
J. D. P. Meldrum
Keyword(s):  
Wreath Product ◽  
Abelian Groups ◽  
Wreath Products ◽  
Nilpotency Class ◽  
Central Series ◽  
Base Group ◽  
Finite Exponent

In this paper we study the structure of the α-central series of the nilpotent wreath product of two Abelian groups, the α-central series being the intersection of the upper central series with the base group. Let C = A wr B, the standard restricted wreath product of A and B. Then Baumslag(1) showed that C is nilpotent if and only if A is a nilpotent p-group of finite exponent and B is a finite p-group for the same prime p. In (5) Liebeck calculated the nilpotency class of the nilpotent wreath product of two Abelian groups. We obtain an expression for an element of the base group to belong to a given term of the upper central series.

scholarly journals COMMUTATIVITY DEGREES OF WREATH PRODUCTS OF FINITE ABELIAN GROUPS

2008 ◽  
Vol 77 (1) ◽  
pp. 31-36 ◽  
Author(s):  
IGOR V. EROVENKO ◽  
B. SURY
Keyword(s):  
Abelian Groups ◽  
Wreath Products ◽  
Conjugacy Classes ◽  
Finite Abelian Groups ◽  
Theoretic Result ◽  
Elementary Number

AbstractWe compute commutativity degrees of wreath products $A \wr B$ of finite Abelian groups A and B. When B is fixed of order n the asymptotic commutativity degree of such wreath products is 1/n2. This answers a generalized version of a question posed by P. Lescot. As byproducts of our formula we compute the number of conjugacy classes in such wreath products, and obtain an interesting elementary number-theoretic result.

Sign in / Sign up

Export Citation Format

Share Document