Typical elements in free groups are in different doubly-twisted conjugacy classes

Christopher P. Staecker

doi:10.1016/j.topol.2010.02.017

Typical elements in free groups are in different doubly-twisted conjugacy classes

Christopher P. Staecker

Fairfield University

Research output: Contribution to journal › Article › peer-review

Abstract

We give an easily checkable algebraic condition which implies that two elements of a finitely generated free group are members of distinct doubly-twisted conjugacy classes with respect to a pair of homomorphisms. We further show that this criterion is satisfied with probability 1 when the homomorphisms and elements are chosen at random.

Original language	American English
Journal	Topology and its Applications
Volume	157
DOIs	https://doi.org/10.1016/j.topol.2010.02.017
State	Published - Jan 1 2010

Keywords

Nielsen theory
Coincidence theory
twisted conjugacy
double-twisted conjugacy
asymptotic density

Disciplines

Computer Sciences
Physical Sciences and Mathematics

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10.1016/j.topol.2010.02.017License: CC BY

Typical elements in free groups are in different doubly-twisted cFinal published version, 162 KBLicense: CC BY

Cite this

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title = "Typical elements in free groups are in different doubly-twisted conjugacy classes",

abstract = " We give an easily checkable algebraic condition which implies that two elements of a finitely generated free group are members of distinct doubly-twisted conjugacy classes with respect to a pair of homomorphisms. We further show that this criterion is satisfied with probability 1 when the homomorphisms and elements are chosen at random.",

keywords = "Nielsen theory, Coincidence theory, twisted conjugacy, double-twisted conjugacy, asymptotic density",

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doi = "10.1016/j.topol.2010.02.017",

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N2 - We give an easily checkable algebraic condition which implies that two elements of a finitely generated free group are members of distinct doubly-twisted conjugacy classes with respect to a pair of homomorphisms. We further show that this criterion is satisfied with probability 1 when the homomorphisms and elements are chosen at random.

AB - We give an easily checkable algebraic condition which implies that two elements of a finitely generated free group are members of distinct doubly-twisted conjugacy classes with respect to a pair of homomorphisms. We further show that this criterion is satisfied with probability 1 when the homomorphisms and elements are chosen at random.

KW - Nielsen theory

KW - Coincidence theory

KW - twisted conjugacy

KW - double-twisted conjugacy

KW - asymptotic density

UR - https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/23

U2 - 10.1016/j.topol.2010.02.017

DO - 10.1016/j.topol.2010.02.017

M3 - Article

VL - 157

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Typical elements in free groups are in different doubly-twisted conjugacy classes

Abstract

Keywords

Disciplines

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