Bacon, Michael R. On the nonabelian tensor square of a nilpotent group of class two. (English) Zbl 0831.20037 Glasg. Math. J. 36, No. 3, 291-296 (1994). If \(G\) is a finitely generated group then \(d(G)\) denotes the minimal number of generators of \(G\). The main results of this paper are Theorem 3.1. Let \(G\) be a nilpotent group of nilpotency class two and \(d(G)=n\). Then \(d(G\otimes G)\leq n(n^2+3n-1)/3\). Theorem 3.2. Let \(G\) be a free \(n\)-generated nilpotent group of class two. Then the free abelian rank of \(G\otimes G\) is \(n(n^2+3n-1)/3\). Reviewer: L.Kurdachenko (Dnepropetrovsk) Cited in 2 ReviewsCited in 5 Documents MSC: 20F05 Generators, relations, and presentations of groups 20F18 Nilpotent groups 20E22 Extensions, wreath products, and other compositions of groups 20E05 Free nonabelian groups Keywords:finitely generated groups; minimal number of generators; nilpotent groups; nilpotency class two; free Abelian rank PDFBibTeX XMLCite \textit{M. R. Bacon}, Glasg. Math. J. 36, No. 3, 291--296 (1994; Zbl 0831.20037) Full Text: DOI References: [1] DOI: 10.1016/0040-9383(87)90004-8 · Zbl 0622.55009 · doi:10.1016/0040-9383(87)90004-8 [2] Brown, C. R. Acad. Sci. Paris Sér. I Math. 298 pp 353– (1984) [3] DOI: 10.2307/1969511 · Zbl 0037.26101 · doi:10.2307/1969511 [4] Bacon, Arch. Math. (Basel) 61 pp 508– (1993) · Zbl 0823.20021 · doi:10.1007/BF01196588 [5] Aboughazi, Bull. Soc. Math. France 115 pp 95– (1987) [6] DOI: 10.1016/0021-8693(87)90248-1 · Zbl 0626.20038 · doi:10.1016/0021-8693(87)90248-1 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.