Finite \(p\)-groups all of whose subgroups of index \(p^3\) are Abelian.

DOI10.1007/s40304-015-0053-2zbMath1322.20012arXiv1410.6226OpenAlexW1980853210MaRDI QIDQ2343045

Qinhai Zhang, Miaomiao Li, Yiqun Shen, Li Bo Zhao

Publication date: 4 May 2015

Published in: Communications in Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.6226

zbMATH Keywords

finite \(p\)-groupsminimal non-Abelian \(p\)-groups\(\mathcal A_t\)-groups

Mathematics Subject Classification ID

Finite nilpotent groups, (p)-groups (20D15)

Related Items (22)

Finite 𝒟C-groups ⋮ Finite 2-groups whose length of chain of nonnormal subgroups is at most 2 ⋮ At-groups with t + 1 generators ⋮ Unnamed Item ⋮ Finite \(p\)-groups with few kernels of nonlinear irreducible characters ⋮ Unnamed Item ⋮ The intersection of nonabelian subgroups of finite p-groups ⋮ Finite \(p\)-groups with few non-major \(k\)-maximal subgroups ⋮ A note on an “Anzahl” theorem of P. Hall ⋮ Finite \(p\)-groups all of whose \(\mathscr{A}_2\)-subgroups are generated by two elements ⋮ Finite \(p\)-groups with a class of complemented normal subgroups ⋮ Finite \(p\)-groups with a minimal non-abelian subgroup of index \(p\). II. ⋮ Finite \(p\)-groups whose nonnormal subgroups have orders at most \(p^3\). ⋮ Finite 2-groups whose number of subgroups of each order are at most \(2^4\) ⋮ Finite \(p\)-groups whose non-normal subgroups have few orders ⋮ Finite \(p\)-groups with a minimal non-abelian subgroup of index \(p\). III. ⋮ A classification of finite metahamiltonian \(p\)-groups ⋮ Intersection of maximal subgroups which are not minimal nonabelian of finite p-groups ⋮ Finite \(p\)-groups all of whose minimal nonabelian subgroups are nonmetacyclic of order \(p^3\) ⋮ The lower bound of the number of nonabelian subgroups of finite p-groups ⋮ Finite \(p\)-groups whose length of chain of nonnormal subgroups is at most 2 ⋮ Finite p-groups all of whose proper subgroups of class 2 are metacyclic

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