Complete solvable group

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This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: complete group and solvable group
View other group property conjunctions OR view all group properties

Definition

A complete solvable group is a group that satisfies both these conditions:

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
solvable group in which every automorphism is inner we no longer require the group to be centerless there exist nilpotent nontrivial groups, such as cyclic group:Z2, in which every automorphism is inner |FULL LIST, MORE INFO
complete group there are complete non-solvable groups such as symmetric group:S5 complete group|complete
solvable group Group whose automorphism group is solvable, Solvable group in which every automorphism is inner|FULL LIST, MORE INFO
group in which every automorphism is inner cyclic group:Z2 Solvable group in which every automorphism is inner|FULL LIST, MORE INFO
group whose automorphism group is solvable |FULL LIST, MORE INFO