Classifying Groups With a Small Number of Subgroups. Issue 3 (16th March 2022)

• Record Type: Journal Article
• Authors: Betz, Alexander; Nash, David A.
• Is Part Of: American Mathematical Monthly. Volume 129:Issue 3(2022)
• Page Start: 255
• Page End: 267
• Publication Date: 2022-03-16
• Subjects: Primary 20E07 -- Secondary 20D20; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/00029890.2022.2010493
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: We provide lower bounds on the number of subgroups of a group G as a function of the primes and exponents appearing in the prime factorization of | G | . Using these bounds, we classify all abelian groups with 22 or fewer subgroups, and all nonabelian groups with 19 or fewer subgroups. This allows us to extend the integer sequence A274847 in the On-Line Encyclopedia of Integer Sequences introduced by Slattery.