Homework Help Overview
The discussion revolves around a group theory problem concerning normal subgroups and their properties within p-groups. The original poster seeks to prove that every subgroup of index p in a group of order p^a is normal.
Discussion Character
- Conceptual clarification, Assumption checking, Mathematical reasoning
Approaches and Questions Raised
- The original poster begins by assuming a subgroup H of index p and questions the implications of H not being normal. They seek guidance on how to proceed from this assumption. Other participants inquire about relevant theorems related to normalizers in p-groups and discuss theorems that may support the original poster's claim.
Discussion Status
The discussion is exploring various theorems related to normalizers in p-groups, with some participants referencing specific results from literature that may lead to the desired conclusion. There is an ongoing examination of the implications of these theorems without reaching a consensus yet.
Contextual Notes
Participants note the importance of the order of the group and the properties of maximal subgroups in the context of the problem. There is an acknowledgment of the need for clarity on theorems being referenced and their applicability to the original question.
)=p but H is not a normal subgroup of G. So for some g in G Hg≠gH. I know I didn't do much, but is this the correct way to start? What to do now?