Philip Hall's problem on non-Abelian splitters
Rüdiger Göbel, Saharon Shelah · Mathematical Proceedings of the Cambridge Philosophical Society · 2003
Philip Hall raised the following question which is stated in The Kourovka Notebook [12, p. 88]: is there a non-trivial group which is isomorphic with every proper extension of itself by itself? We will split the problem into two parts: we want to find non-commutative splitters, that are groups with cartesian product is a splitter and hence obviously a Hall group in the above sense. Then we will apply a recent result from our joint paper [9] which also shows that such groups exist; in fact there is a class of Hall groups which is not a set.