ABSTRACT
This paper extends results from the author’s earlier paper [8] where the circumstances under which there could or could not be a permutation embedding of one infinite permutation group into another were studied in terms of natural criteria on the supports. Here we rather focus on the question of ‘how many’ ways (in the sense of Baire category) two such groups can be jointly embedded. In three out of the four cases studied in [8] the family of suitable embeddings is comeagre, but in the fourth is meagre, answering a question of P.J.Cameron.
