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Q-tensor Square of Finitely Generated Nilpotent Groups, Q >= 0 by Rocco, Noraí R.; Rodrigues, Eunice C. P. is a scholarly article available to read on EtoBox.

What is Q-tensor Square of Finitely Generated Nilpotent Groups, Q >= 0 about?

The authors extend to the $q-$tensor square $G \otimes^q G$ 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 $G \otimes G$ ($q = 0$). The results are applied to the computation of $G \otimes^q G$ for finitely generated nilpotent groups $G$, specially for free nilpotent groups of finite rank. They also generalize to all $q \geq 0$ results of M. Bacon regarding an upper bound to the minimal number of generators of the non-abelian tensor square $G \otimes G$ 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, $n \geq 2$, for all $q \geq 0.$ This shows that the above mentioned upper bound is also achieved for these groups when $q > 1.$

Author

Rocco, Noraí R.; Rodrigues, Eunice C. P.

Published

2016

Language

EN