Abelian marginal subgroup

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

Definition

A subgroup H of a group G is termed an abelian marginal subgroup if H is an abelian group (i.e., it is an abelian subgroup of G) and H is also a marginal subgroup of G.

Examples

Examples in small finite groups

Here are some examples of subgroups in basic/important groups satisfying the property:


Here are some examples of subgroups in relatively less basic/important groups satisfying the property:

 Group partSubgroup partQuotient part
Center of dihedral group:D8Dihedral group:D8Cyclic group:Z2Klein four-group

Here are some examples of subgroups in even more complicated/less basic groups satisfying the property:

 Group partSubgroup partQuotient part
Center of M16M16Cyclic group:Z4Klein four-group
Center of direct product of D8 and Z2Direct product of D8 and Z2Klein four-groupKlein four-group

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
marginal subgroup of abelian group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
abelian characteristic subgroup abelian and a characteristic subgroup: invariant under all automorphisms |FULL LIST, MORE INFO
abelian normal subgroup abelian and a normal subgroup: invariant under all inner automorphisms |FULL LIST, MORE INFO