## Is the Tensor/Exterior square G⊗GG\otimes G or G∧GG\wedge G of infinite p-group also a p-group?

Let G be an infinite countable p-group. Is it true that G⊗G or G∧G are also p-groups? (where G acts on itself by conjugation). For simplicity, you can consider that G=[G,G], and then the above groups are isomorphic to the Universal Schur Cover. I am very frustrated, because a lot of websites and papers say … Read more