Let $G$ be a finite group having the property that for any prime $p$ dividing $|G|$, it has a subgroup H with $[G:H]=p$. What can be said about these groups? I believe I can prove that they must be solvable. But are they supersolvable?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top