Solvable not implies solvable automorphism group
This article gives the statement and possibly, proof, of a non-implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., solvable group) need not satisfy the second group property (i.e., group whose automorphism group is solvable)
View a complete list of group property non-implications | View a complete list of group property implications
Get more facts about solvable group|Get more facts about group whose automorphism group is solvable
Further information: endomorphism structure of elementary abelian group:E8
Let be elementary abelian group:E8, which is a three-dimensional vector space over field:F2. The automorphism group is GL(3,2), which is a finite simple non-abelian group of order 168, hence is not solvable.