A finite abelian p-group (Exercise 7) is generated by its elements of maximal order.

Data from Exercise 7

A (sub)group in which every element has order a power of a fixed prime p is  called a p-(sub)group.(a) G(p) is the unique maximum p-subgroup of G (that is, every p-subgroup of  G is contained in G(p)).(b) where the sum is over all primes p such that G(p) ≠ 0.

Transcribed Image Text:

G = G(p),