Finitely generated 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: finitely generated group and periodic group
View other group property conjunctions OR view all group properties

Definition

Symbol-free definition

A finitely generated periodic group is a group satisfying the following two conditions:

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finite group Follows from periodic not implies locally finite (see also examples: Grigorchuk group, infinite Burnside groups, and Tarski monsters) Finitely presented periodic group|FULL LIST, MORE INFO
Finitely presented periodic group both periodic and finitely presented; conjectured to be equivalent to being a finite group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Periodic group |FULL LIST, MORE INFO
Finitely generated group |FULL LIST, MORE INFO
Group generated by finitely many periodic elements |FULL LIST, MORE INFO