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 An explicit formula for the number of subgroups of a finite abelian $p$-group up to rank $3$ Commun. Korean Math. Soc. 2013 Vol. 28, No. 4, 649-667 https://doi.org/10.4134/CKMS.2013.28.4.649Printed October 1, 2013 Ju-Mok Oh Gangneung-Wonju National University Abstract : In this paper we give an explicit formula for the total number of subgroups of a finite abelian $p$-group up to rank three. Keywords : enumeration, subgroup, abelian $p$-group Downloads: Full-text PDF