On Hua-Tuan's conjecture. II.
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 \(\{0,1,2,\dots,p-1\}\).)
scientific article; zbMATH DE number 5916771