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
Definition
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).
Examples
- The Tarski monsters are examples of simple periodic groups.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| 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 |