Template:Random funky category

Category:Characteristic subgroup-closed group properties: A list of group properties that are characteristic subgroup-closed: any characteristic subgroup of a group with the property also has the property.@@@Category:Applications of characteristic of normal implies normal: Some results that apply the fact that any characteristic subgroup of a normal subgroup is normal.@@@Category:Commutator computations: Facts about properties of the commutator of two subsets, or between a subgroup and a subset, in terms of the properties of the original subsets.@@@Category:Existence statements about arbitrarily large subnormal depth: Facts that guarantee the existence of subnormal subgroups of arbitrarily large subnormal depth satisfying certain additional conditions.@@@Category:Constraints on numerical invariants for finite groups: A list of constraints that can be placed on numerical invariants associated with finite groups.@@@Category:Congruence conditions: A list of the many statements in group theory that involve congruence conditions.@@@Category:Facts about odd-order groups that break down for even-order groups: A list of facts that are true for the finite odd-order groups but break down (in general) for groups of even order.@@@Category:Facts about groups of coprime order whose proof requires the assumption that one of them is solvable: These facts are true for all finite groups because coprime implies one is solvable, a consequence of the odd-order implies solvable.