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On the nonabelian tensor square of a nilpotent group of class two. (English) Zbl 0831.20037

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 \(n(n^2+3n-1)/3\).

MSC:

20F05 Generators, relations, and presentations of groups
20F18 Nilpotent groups
20E22 Extensions, wreath products, and other compositions of groups
20E05 Free nonabelian groups
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[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
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