Useful Lemmas for p-Groups

This lecture covers useful lemmas for p-groups, including Lemma 2.4 which states that if p divides the index of every proper subgroup of a group G, then p also divides the order of the center of G. Additionally, Lemma 2.5 shows that in a finite abelian group G with p dividing its order, there exists an element a such that the order of a is p.