Hatcher-Topology-of-Numbers · Problem 7.3.4

The Class Group for Quadratic Forms

Mathematics — Algebraic Topology · maximum-order-in-finite-abelian-group

Problem

Determine the maximum order of elements of a finite abelian group

G

in terms of the factorization of

G

as a product of cyclic groups of prime power order, and show that the orders of elements of

G

are exactly all the divisors of this maximal order.