Abstract

This is a progress report on some of the developments in nonabelian tensor products of groups since the appearance of the paper “Some Computations of Non-Abelian Tensor Products of Groups” by Brown, Johnson and Robertson, ten years ago.

In the spring of 1988 Ronnie Brown came to Binghamton and gave a talk about nonabelian tensor products, in particular about his paper with Johnson and Robertson [7] which had just appeared. I fell in love with tensor products on first sight and started my student Michael Bacon on this topic for his dissertation, and since then others have joined in these investigations.

This talk is an invitation for others to join in this research. There are many interesting and accessible problems and it appears likely that there are interesting applications to group theory, in the same way as regular tensors have been applied.

All this is provided you do not immediately get thrown off by the notation. In context with nonabelian tensor products left actions are used. Early on I contemplated switching to right action but decided against it. That would be like insisting on driving on the right in a country where everyone else drives on the left.

We use the following notation. For elements g,g′,h,h′ in a group G we set hg = hgh−1 for the conjugate of g by h, and [h,g] = hgh−1g−1 for the commutator of h and g.