| Abstract: | For a finite set V and a positive integer k with  , letting  be the set of all k‐subsets of V, the pair  is called the complete k‐hypergraph on V, while each k‐subset of V is called an edge. A factorization of the complete k‐hypergraph  of index  , simply a  ‐factorization of order n, is a partition  of the edges into s disjoint subsets such that each k‐hypergraph  , called a factor, is a spanning subhypergraph of  . Such a factorization is homogeneous if there exist two transitive subgroups G and M of the symmetric group of degree n such that G induces a transitive action on the set  and M lies in the kernel of this action. In this article, we give a classification of homogeneous factorizations of  that admit a group acting transitively on the edges of  . It is shown that, for  and  , there exists an edge‐transitive homogeneous  ‐factorization of order n if and only if  is one of (32, 3, 5), (32, 3, 31), (33, 4, 5),  , and  , where  and q is a prime power with  . |
