Simple periodic group

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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).


Relation with other properties

Stronger 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