Recently, Burns and Goldsmith  characterized the maximal order Abelian subgroups of the symmetric groups using elementary techniques and the results of Hoffman . This classification could also be directly inferred from the results of Kovacs and Praeger . A natural extension would be to consider the weaker, more general form of commutativity, three-rewriteability. The purpose of this paper is to completely characterize the maximal order three-rewriteable subgroups of the symmetric groups.
O'Bryan, John T., "Maximal Order Three-Rewriteable Subgroups of Symmetric Groups" (1990). Mathematical Sciences Technical Reports (MSTR). 140.