Normal not implies subgroup-conjugating

From Groupprops
Jump to: navigation, search
This article gives the statement and possibly, proof, of a non-implication relation between two automorphism properties. That is, it states that every automorphism satisfying the first automorphism property (i.e., normal automorphism) need not satisfy the second automorphism property (i.e., subgroup-conjugating automorphism)
View a complete list of automorphism property non-implications | View a complete list of automorphism property implications
Get more facts about normal automorphism|Get more facts about subgroup-conjugating automorphism


A normal automorphism of a group (an automorphism that preserves all the normal subgroups) need not be subgroup-conjugating -- it need not send every subgroup to a conjugate subgroup.

Related facts

Stronger facts

Facts used

  1. Class-preserving not implies subgroup-conjugating
  2. Class-preserving implies normal


The proof follows directly by piecing together facts (1) and (2).