The nonabelian tensor square of a 2-generatorp-group of class 2

On the Capability of Finitely Generated Non-Torsion Groups of Nilpotency Class 2

“…We start with some tensor expansion formulas for groups of nilpotency class 2, which can be found in Proposition 3.2 and Lemma 3.4 of [2]. LEMMA 2.1.…”

“…In [1], a new classification for two-generator p-groups of nilpotency class 2 is given that corrects and simplifies previous classifications published in [2,11,16]. Based on this new classification, Magidin and Morse give a complete determination of all capable two-generator p-groups of class 2, using a unified approach and modified tensor methods [14].…”

On Computing the Non-Abelian Tensor Squares of the Free 2-Engel Groups

“…, g n of E. We start with two-and three-variable identities that hold in the tensor square of a 2-Engel group and its subgroups. The proofs of these identities can be found in [3,4]. Lemma 2.4.…”

“…[8], in which they compute G ⊗ G for all groups of order up to thirty. Subsequent papers investigate explicit descriptions of the non-abelian tensor square for particular groups; for nilpotent of class 2 groups see [1][2][3]13,16], for metacyclic groups see [5,14], and for linear groups see [12]. A recent survey article on the non-abelian tensor squares and the more general non-abelian tensor products of groups can be found in [15].…”

“…In [1,2], the non-abelian tensor squares of nilpotent of class 2 groups were investigated. The non-abelian tensor square of the free nilpotent group of class 2 and rank 2, which is exactly the free 2-Engel group of rank 2, was shown to be free abelian of rank 6.…”