group theoryabstract algebrapigeonhole principlesuperior algebrasuperior algebra unsolved
Problem Statement
For any n∈N∗, let Hn={n!k∣k∈Z}. a) Prove that Hn is a subgroup of the group (Q,+) and that Q=⋃n∈N∗Hn;b) Prove that if G1,G2,…,Gm are subgroups of the group (Q,+) and Gi=Q,(∀)1≤i≤m, then G1∪G2∪…∪Gm=QMarian Andronache & Ion Savu