Wang, Yulei; Zhang, Yuanfeng; Guo, Peng Factorization numbers of a class of finite \(p\)-groups. (English) Zbl 1438.20027 Chin. Q. J. Math. 33, No. 4, 434-440 (2018). Summary: Let \(p\) be a prime number and \({f_2} (G)\) be the number of factorizations \(G = AB\) of the group \(G\), where \(A\), \(B\) are subgroups of \(G\). Let \(G\) be a class of finite \(p\)-groups as follows, \(G = \langle a, b|a^{p^n} = b^{p^m} = 1, a^b = a^{p^{n-1}+1}\rangle\), where \(n > m \ge 1\). In this article, the factorization number \({f_2} (G)\) of \(G\) is computed, which improves the results in literature. MSC: 20D60 Arithmetic and combinatorial problems involving abstract finite groups 20D40 Products of subgroups of abstract finite groups 20D15 Finite nilpotent groups, \(p\)-groups Keywords:finite \(p\)-group; factorization number; subgroup commutativity degree PDFBibTeX XMLCite \textit{Y. Wang} et al., Chin. Q. J. Math. 33, No. 4, 434--440 (2018; Zbl 1438.20027) Full Text: DOI