Torsion-free group with two conjugacy classes: Difference between revisions

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{{group property conjunction|aperiodic group|group with two conjugacy classes}}
{{group property conjunction|torsion-free group|group with two conjugacy classes}}


==Definition==
==Definition==
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===Symbol-free definition===
===Symbol-free definition===


A '''torsion-free group with two conjugacy classes''' or '''aperiodic group with two conjugacy classes''' is a nontrivial group satisfying these two conditions: it is [[aperiodic group|aperiodic]], i.e., no nontrivial element in it has finite order, and [[group with two conjugacy classes|it has two conjugacy classes of elements]].
A '''torsion-free group with two conjugacy classes''' or '''aperiodic group with two conjugacy classes''' is a nontrivial group satisfying these two conditions: it is [[torsion-free group|torsion-free]], i.e., no nontrivial element in it has finite order, and [[group with two conjugacy classes|it has two conjugacy classes of elements]].


==Relation with other properties==
==Relation with other properties==

Latest revision as of 19:39, 26 May 2010

This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: torsion-free group and group with two conjugacy classes
View other group property conjunctions OR view all group properties

Definition

Symbol-free definition

A torsion-free group with two conjugacy classes or aperiodic group with two conjugacy classes is a nontrivial group satisfying these two conditions: it is torsion-free, i.e., no nontrivial element in it has finite order, and it has two conjugacy classes of elements.

Relation with other properties

Weaker properties

Facts