Counting the Subgroups of Some Finite Groups

DOI10.2307/2323503zbMath1303.20024OpenAlexW2036358336MaRDI QIDQ2928593

William C. Calhoun

Publication date: 10 November 2014

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2323503

zbMATH Keywords

numbers of subgroupsfinite metacyclic groups

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Series and lattices of subgroups (20D30)

Related Items (13)

Cyclicity degrees of finite groups. ⋮ Unnamed Item ⋮ How Hamiltonian can a finite group be? ⋮ Addendum to ``Subgroup commutativity degrees of finite groups. ⋮ Probabilistic aspects of ZM-groups ⋮ The Chermak-Delgado lattice of ZM-groups ⋮ Unnamed Item ⋮ On \(n\)-cyclic groups ⋮ On a divisibility property involving the sum of element orders ⋮ Finite non-cyclic \(p\)-groups whose number of subgroups is minimal ⋮ The normal subgroup structure of ZM-groups. ⋮ On the number of subgroups of non-metacyclic minimal non-abelian p-groups ⋮ Representing and counting the subgroups of the group \(\mathbb{Z}_m \times \mathbb{Z}_n\)

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