MAXIMAL ABELIAN SUBGROUPS OF THE FINITE SYMMETRIC GROUP

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Konieczny Janusz

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2021 | Volume:10 | Issue:3 Page(s): 103-124

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Title

MAXIMAL ABELIAN SUBGROUPS OF THE FINITE SYMMETRIC GROUP

Author(s)

Konieczny Janusz | Issue Writer Certificate

Keywords

Symmetric groups

maximal abelian subgroups

second centralizers

abelian rank

Abstract

Let G be a group. For an element a 2 G, denote by C (a) the second centralizer of a in G, which is the set of all elements b 2 G such that bx = xb for every x 2 G that commutes with a. Let M be any maximal abelian subgroup of G. Then C 2 2 (a) ,M for every a 2 M. The abelian rank (a-rank) of M is the minimum cardinality of a set A ,M such that ∪,2 C a 2 A (a) generates M. Denote by Sn the symmetric group of permutations on the set X = f 1, : : :, n g. 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.

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APA: Copy

Konieczny, Janusz. (2021). MAXIMAL ABELIAN SUBGROUPS OF THE FINITE SYMMETRIC GROUP. INTERNATIONAL JOURNAL OF GROUP THEORY, 10(3), 103-124. SID. https://sid.ir/paper/1004165/en

Vancouver: Copy

Konieczny Janusz. MAXIMAL ABELIAN SUBGROUPS OF THE FINITE SYMMETRIC GROUP. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2021;10(3):103-124. Available from: https://sid.ir/paper/1004165/en

IEEE: Copy

Janusz Konieczny, “MAXIMAL ABELIAN SUBGROUPS OF THE FINITE SYMMETRIC GROUP,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 10, no. 3, pp. 103–124, 2021, [Online]. Available: https://sid.ir/paper/1004165/en

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