ON GROUPS ALL OF WHOSE PROPER SUBGROUPS ARE FINITE CYCLIC

Abstract

For any odd number n≥1003, the authors construct an infinite 2-generator group each of whose proper subgroups is contained in a cyclic subgroup of order n. This result strengthens analogous results of Ol'shanskiĭ for prime n>1075 and Atabekyan and Ivanov for odd n>1080. The proof is carried out in the original language of Novikov-Adyan theory. Bibliography: 6 titles.