Solvable group in which every automorphism is inner
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: solvable group and group in which every automorphism is inner
View other group property conjunctions OR view all group properties
Definition
A solvable group in which every automorphism is inner is a group that is both a solvable group and a group in which every automorphism is inner.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| complete solvable group | must also be a centerless group | |FULL LIST, MORE INFO | ||
| nilpotent group in which every automorphism is inner | must be a nilpotent group as well | nilpotent implies solvable | there exist nontrivial solvable complete groups | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| solvable group | ||||
| group in which every automorphism is inner |