Torsion-free group with two conjugacy classes: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A '''torsion-free 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]]. | 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== | |||
===Weaker properties=== | |||
* [[Stronger than::Simple torsion-free group]] | |||
==Facts== | |||
* [[Every torsion-free group is a subgroup of a torsion-free group with two conjugacy classes]] | |||
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.