Periodic subgroup

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This article describes a property that arises as the conjunction of a subgroup property: subgroup with a group property (itself viewed as a subgroup property): periodic group
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a periodic subgroup if the subgroup is a periodic group viewed as a group in its own right, i.e., every element of the subgroup has finite order.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finite subgroup
subgroup of finite group
subgroup of periodic group

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
local powering-invariant subgroup periodic implies local powering-invariant Intermediately local powering-invariant subgroup|FULL LIST, MORE INFO
powering-invariant subgroup periodic implies powering-invariant any aperiodic group as a subgroup of itself Intermediately local powering-invariant subgroup, Intermediately powering-invariant subgroup, Local powering-invariant subgroup|FULL LIST, MORE INFO