Maximal Abelian Subgroups of the Finite Symmetric Group

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International Journal of Group Theory

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Let G be a group. For an element a ∈ G, denote by C 2 (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 C 2 (a) ⊆ M for every a ∈ M. The abelian rank (a-rank) of M is the minimum cardinality of a set A ⊆ M such that ∪ a∈A C 2 (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 Sn of a-rank 1 and describe a class of maximal abelian subgroups of Sn of a-rank at most 2.


The International Journal of Group Theory (IJGT) is a publication of the University of Isfahan in English. IJGT is an international mathematical journal founded in 2011. It carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.

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