Cyclic isomorph-containing subgroup
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 | |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 |