Log-Space Complexity of the Conjugacy Problem in Wreath Products

2017 ◽  
pp. 215-236 ◽  
Author(s):  
Alexei Myasnikov ◽  
Svetla Vassileva ◽  
Armin Weiss
Keyword(s):  
Conjugacy Problem ◽  
Wreath Products ◽  
Space Complexity

Log-space conjugacy problem in the Grigorchuk group

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Alexei Miasnikov ◽  
Svetla Vassileva
Keyword(s):  
Conjugacy Problem ◽  
Space Complexity ◽  
Grigorchuk Group

AbstractIn this paper we prove that the conjugacy problem in the Grigorchuk group Γ has log-space complexity.

scholarly journals The geometry of the conjugacy problem in wreath products and free solvable groups

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Andrew W. Sale
Keyword(s):  
Quotient Group ◽  
Solvable Groups ◽  
Conjugacy Problem ◽  
Wreath Products ◽  
Length Function ◽  
Effective Version ◽  
Group A ◽  
Definition Of

AbstractIn this paper, we describe an effective version of the conjugacy problem and study it for wreath products and free solvable groups. The problem involves estimating the length of short conjugators between two elements of the group, a notion which leads to the definition of the conjugacy length function. We show that for free solvable groups the conjugacy length function is at most cubic. For wreath products the behaviour depends on the conjugacy length function of the two groups involved, as well as subgroup distortion within the quotient group.

The Conjugacy Problem in Free Solvable Groups and Wreath Products of Abelian Groups is in TC0

2018 ◽  
Vol 63 (4) ◽  
pp. 809-832
Author(s):  
Alexei Miasnikov ◽  
Svetla Vassileva ◽  
Armin Weiß
Keyword(s):  
Abelian Groups ◽  
Solvable Groups ◽  
Conjugacy Problem ◽  
Wreath Products

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products

Generalized wreath products of $m$-groups

2019 ◽  
Vol 58 (2) ◽  
pp. 167-178
Author(s):  
A. V. Zenkov ◽  
O. V. Isaeva
Keyword(s):  
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.

scholarly journals RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY

2021 ◽  
pp. 1-37
Author(s):  
Martijn Caspers
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Riesz Transform ◽  
Wreath Products ◽  
Compact Quantum Group ◽  
Riesz Transforms ◽  
Markov Semigroup ◽  
Markov Semigroups ◽  
Free Products ◽  
Compact Quantum Groups

Abstract One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups of central multipliers on a compact quantum group which we shall call ‘approximate linearity with almost commuting intertwiners’. We show that this property is stable under free products, monoidal equivalence, free wreath products and dual quantum subgroups. Examples include in particular all the (higher-dimensional) free orthogonal easy quantum groups. We then show that a compact quantum group with a quantum Markov semigroup that is approximately linear with almost commuting intertwiners satisfies the immediately gradient- ${\mathcal {S}}_2$ condition from [10] and derive strong solidity results (following [10]). Using the noncommutative Riesz transform we also show that these quantum groups have the Akemann–Ostrand property; in particular, the same strong solidity results follow again (now following [27]).

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