Strongly p-solvable implies Glauberman type for odd p

Statement
Suppose $$p$$ is an odd prime and $$G$$ is a strongly p-solvable group. Then, $$G$$ is a group of Glauberman type for the prime $$p$$.

In particular, for $$p \ge 5$$, any fact about::p-solvable group is of Glauberman type for $$p$$.

Facts used

 * 1) uses::p-solvable implies p-constrained (along with the fact that strongly p-solvable by definition implies p-solvable)
 * 2) uses::strongly p-solvable implies p-stable
 * 3) uses::p-constrained and p-stable implies Glauberman type for odd p

Proof
The proof follows directly by combining facts (1), (2), and (3).