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   maximal abelian subgroups of the finite symmetric group  
   
نویسنده konieczny janusz
منبع international journal of group theory - 2021 - دوره : 10 - شماره : 3 - صفحه:103 -124
چکیده    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.
کلیدواژه symmetric groups ,maximal abelian subgroups ,second centralizers ,abelian rank.
آدرس university of mary washington, department of mathematics, usa
پست الکترونیکی jkoniecz@umw.edu
 
     
   
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