Centers of centralizer nearrings determined by inner automorphisms of symmetric groups

Boudreaux, M.; Cannon, G.; Neuerburg, K.; Palmer, T.; Troxclair, T.

doi:10.22124/jart.2020.14757.1171

Centers of centralizer nearrings determined by inner automorphisms of symmetric groups

Document Type : Research Paper

Authors

M. Boudreaux
G. Cannon
K. Neuerburg
T. Palmer
T. Troxclair

Department of Mathematics, Southeastern Louisiana University, Hammond, LA, 70402, USA.

10.22124/jart.2020.14757.1171

Abstract

The question of identifying the elements of the center of a nearring and of determining when that center is a subnearring is an area of continued research. We consider the centers of centralizer nearrings,

M_{I} (S_{n})

, determined by the symmetric groups

S_{n}

with

n \geq 3

and the inner automorphisms

I = I n n S_{n}

. General tools for determining elements of the center of

M_{I} (S_{n})

are developed, and we use these to list the specific elements in the centers of

M_{I} (S_{4})

M_{I} (S_{5})

, and

M_{I} (S_{6})

Keywords

Centralizer nearring
center
inner automorphisms
symmetric groups

Volume 8, Issue 1
June 2020
Pages 51-65

Centers of centralizer nearrings determined by inner automorphisms of symmetric groups

Volume 8, Issue 1June 2020Pages 51-65

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Volume 8, Issue 1
June 2020
Pages 51-65