Simple periodic group
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: simple group and periodic group
View other group property conjunctions OR view all group properties
A simple periodic group (also called simple torsion group or periodic simple group or torsion simple group) is a group that is both a simple group (i.e., it is nontrivial and has no proper nontrivial normal subgroups) and a periodic group (i.e., every element in it has finite order).
- The Tarski monsters are examples of simple periodic groups.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|Finite simple group||Locally finite simple group|FULL LIST, MORE INFO|
|Locally finite simple group||simple as well as locally finite: every finitely generated subgroup is finite|||FULL LIST, MORE INFO|