Groups of square-free order are scarce

Michael Ellsworth Mays

Vol. 91 (1980), No. 2, 373–375

DOI: 10.2140/pjm.1980.91.373

Abstract

We devise an upper bound for B(n), the number of nonisomorphic groups whose orders are square-free and no larger than n, and a lower bound for T(n), the number of nonisomorphic groups whose orders are no larger than n. It is then noted that B(n) = o(T(n)).

Mathematical Subject Classification 2000

Primary: 20D60

Milestones

Received: 27 February 1978

Revised: 27 August 1979

Published: 1 December 1980