Template:Random interesting definition

Permutable subgroup (DEFINITION): A subgroup that permutes with every other subgroup. May not be normal.@@@Hall subgroup (DEFINITION): A subgroup of a finite group whose order and index are relatively prime. Sylow subgroups are a special case.@@@Complete group (DEFINITION): A group whose center is trivial and for which every automorphism is inner.@@@Class-preserving automorphism: An automorphism of a group that sends every element to within its conjugacy class. May not be inner.@@@Baer norm (DEFINITION): The intersection of the normalizers of all subgroups of the group. Contains the center, and is a hereditarily normal subgroup.@@@Highly transitive group action (DEFINITION): A group action that is $$k$$-transitive for all natural numbers $$k$$.@@@Subnormal series: An ascending (resp., descending) series of subgroups with each subgroup normal in its successor (resp., predecessor).@@@Transitive subgroup property (DEFINITION): A subgroup satisfying the property inside a subgroup satisfying the property satisfies the property.