Q-tensor square of finitely generated nilpotent groups, q >= 0

2016/03/17 by Rocco, Noraí R., Rodrigues, Eunice C. P.
#20E26 #20F15 #20F40 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1603.05424

Abstract

The authors extend to the q-tensor square G ⊗^q G of a group G, q a non-negative integer, some structural results due to R. D. Blyth, F. Fumagalli and M. Morigi concerning the non-abelian tensor square G ⊗ G (q = 0). The results are applied to the computation of G ⊗^q G for finitely generated nilpotent groups G, specially for free nilpotent groups of finite rank. They also generalize to all q ≥ 0 results of M. Bacon regarding an upper bound to the minimal number of generators of the non-abelian tensor square G ⊗ G when G is a n-generator nilpotent group of class 2. The paper ends with the computation of the q-tensor squares of the free n-generator nilpotent group of class 2, n ≥ 2, for all q ≥ 0. This shows that the above mentioned upper bound is also achieved for these groups when q > 1.

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