P-normal not implies p-solvable
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., p-normal group) need not satisfy the second subgroup property (i.e., p-solvable group)
View a complete list of subgroup property non-implications | View a complete list of subgroup property implications
Get more facts about p-normal group|Get more facts about p-solvable group
EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property p-normal group but not p-solvable group|View examples of subgroups satisfying property p-normal group and p-solvable group
Example of the alternating group of degree five
Further information: alternating group:A5
The alternating group of degree five is a -normal group for all primes , because all its Sylow subgroups are abelian. On the other hand, since the group is simple non-abelian, it is not -solvable for .