Maximal abelian subgroups of the finite symmetric group

Let G be a group. For an element a∈G, denote by /cs(a) the second centralizer of~a in~G, which is the set of all elements b∈G such that bx=xb for every x∈G that commutes with a. Let M be any maximal abelian subgroup of G. Then /cs(a)⊆M for every a∈M. The /emph{abelian rank} (/emph{a-rank}) of M is the minimum cardinality of a set A⊆M such that ⋃a∈A/cs(a) generates M. Denote by Sn the symmetric group of permutations on the set X={1,…,n}. The aim of this paper is to determine the maximal abelian subgroups of /gx of /cor~1 and describe a class of maximal abelian subgroups of /gx of /cor at most~2. Keywords