On Hua-Tuan's conjecture. II. (Q547334)
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scientific article; zbMATH DE number 5916771
| Language | Label | Description | Also known as |
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| English | On Hua-Tuan's conjecture. II. |
scientific article; zbMATH DE number 5916771 |
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On Hua-Tuan's conjecture. II. (English)
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1 July 2011
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According to Kulakoff's theorem, the number of nontrivial subgroups in a noncyclic \(p\)-group \(G\) is equal to \(1+p+kp^2\) for some nonnegative integer. More than 60 years ago Hua and Tuan conjectured that \(k\in\{0,1,2\}\). The authors in this and the previous paper [part I, ibid. 52, No. 2, 389-393 (2009; Zbl 1181.20019)] constructed \(p\)-groups with \(k=3\). They conjectured that \(k\in\{0,1,2,3\}\). The paper is devoted to checking this conjecture for a number of small \(p\)-groups. (I think that \(k\) can be equal to every member of the set \(\{0,1,2,\dots,p-1\}\).)
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finite \(p\)-groups
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numbers of subgroups
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Hua-Tuan conjecture
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\(p\)-groups of maximal class
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enumerations of subgroups
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Magma package
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