Difference between revisions of "Finite subnormal subgroup"

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

Definition

A subgroup of a group is termed a finite subnormal subgroup if it is finite as a group and subnormal as a subgroup.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finite characteristic subgroup the subgroup is both a finite group and a characteristic subgroup (characteristic implies subnormal, via normal) use normal not implies characteristic (finite examples) Finite normal subgroup|FULL LIST, MORE INFO
Finite normal subgroup the subgroup is both a finite group and a normal subgroup (normal implies subnormal) normality is not transitive (finite examples) |FULL LIST, MORE INFO
Subnormal subgroup of finite group subnormal subgroup where the whole group is a finite group |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finitely generated subnormal subgroup |FULL LIST, MORE INFO
Subnormal subgroup Right-transitively fixed-depth subnormal subgroup|FULL LIST, MORE INFO