O quadrado tensorial não abeliano e outros funtores homológicos de p-grupos finitos powerful
finite p-group, powerful p-group, non-abelian tensor product, non-abelian
tensor square.
This work aims to present results on the non-abelian tensor square G ⊗ G of a group
G, for the class of powerful finite p-groups. Some properties and results about finite
p-groups and powerful p-groups that will be used in the context will also be presented,
as well as the main properties of the group ν(G), a certain extension of G ⊗ G by
G × G. In addition, we will address some bounds for the order, the exponent and the
rank of G ⊗ G and of the non-abelian exterior square G ∧ G for finite p-groups G.