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Computers, trees and Abelian groups

1988
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Computers and Mathematics with Applications
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The problem of classifying pairs consisting of a finite Abelian group and a subgroup leads to the study of rooted trees whose nodes are decorated with natural numbers that strictly increase as you go towards the root. The lattices of trees that correspond to indecomposable pairs that are bounded by pn were generated by computer up to n = 6. As a result, an unexpected, almost complete, duality was discovered in these lattices. The structure of a finite Abelian group is completely described by

doi:10.1016/0898-1221(88)90220-9
fatcat:6ihtucttcrbz7mayd34q563rum