Normal-extensible not implies inner
This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., normal-extensible automorphism) need not satisfy the second subgroup property (i.e., inner automorphism)
View a complete list of subgroup property non-implications | View a complete list of subgroup property implications
Get more facts about normal-extensible automorphism|Get more facts about inner automorphism
EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property normal-extensible automorphism but not inner automorphism|View examples of subgroups satisfying property normal-extensible automorphism and inner automorphism
Given fact (1), we simply need to exhibit a group satisfying the condition of being centerless and maximal in its automorphism group. One example is the alternating group of degree four.