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

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 |FULL LIST, MORE INFO
* Cyclic 1-automorphism-invariant subgroup |FULL LIST, MORE INFO
Quasiautomorphism-invariant subgroup |FULL LIST, MORE INFO
* Cyclic quasiautomorphism-invariant subgroup |FULL LIST, MORE INFO
Cyclic characteristic subgroup |FULL LIST, MORE INFO
Cyclic normal subgroup |FULL LIST, MORE INFO
Characteristic subgroup |FULL LIST, MORE INFO
Normal subgroup |FULL LIST, MORE INFO