In this paper, groups of order p n in which the number of subgroups of possible order is less than or equal to p 3 are classified. It turns out that if p > 2, n ≥ 5, then the classification of groups of order p n in which the number of subgroups of possible order is less than or equal to p 3 and the classification of groups of order p n with a cyclic subgroup of index p 2 are the same.
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Project supported by the National Natural Science Foundation of China (No. 10671114), the Shanxi Provincial Natural Science Foundation of China (No. 2008012001) and the Returned Abroad-Student Fund of Shanxi Province (No. 13-56).
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Qu, H., Sun, Y. & Zhang, Q. Finite p-groups in which the number of subgroups of possible order is less than or equal to p 3 . Chin. Ann. Math. Ser. B 31, 497–506 (2010). https://doi.org/10.1007/s11401-010-0590-7
- Inner abelian p-groups
- Metacyclic p-groups
- Groups of order p n with a cyclic subgroup of index p 2
- The number of subgroups
2000 MR Subject Classification