Locally finite simple group
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: locally finite group and simple group
View other group property conjunctions OR view all group properties
Definition
A locally finite simple group is a group that is both a locally finite group and a simple group.
Examples
- Every finite simple group is a locally finite simple group.
- The finitary alternating group on an infinite set is a locally finite simple group.
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 |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Locally finite group | |FULL LIST, MORE INFO | |||
| Simple group | |FULL LIST, MORE INFO | |||
| Periodic simple group | simple group where every element has finite order | |FULL LIST, MORE INFO |