Core-free permutable subgroup

This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: core-free subgroup and permutable subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup of a group is termed a core-free permutable subgroup if it is both core-free (i.e., its normal core is trivial) and permutable (i.e., quasinormal).

Relation with other properties

Stronger properties

• Core-free permutable subnormal subgroup

Weaker properties

• Core-free subgroup
• Permutable subgroup