Cyclic isomorph-containing subgroup

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

Definition

A subgroup of a group is termed a cyclic isomorph-containing subgroup if is a cyclic group and is an isomorph-containing subgroup of , i.e., every subgroup of isomorphic to is contained in .

Relation with other properties

Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Cyclic homomorph-containing subgroup

Weaker properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
1-automorphism-invariant subgroup |
* Cyclic 1-automorphism-invariant subgroup |
Quasiautomorphism-invariant subgroup |
* Cyclic quasiautomorphism-invariant subgroup |
Cyclic characteristic subgroup |
Cyclic normal subgroup |
Characteristic subgroup |
Normal subgroup |