TY - JOUR

T1 - Generalization of the basis theorem for alternating groups

AU - Shvartz, R.

AU - Fanrazi, L.

AU - Khazkeia, S.

N1 - Publisher Copyright:
© 2023 Women, Gender and Research. All rights reserved.

PY - 2019

Y1 - 2019

N2 - There were defined in the paper of Robert Shwartz [3] OGS for symmetric groups, as an interesting generalization of the basis of finite abelian groups. The definition of OGS states that that every element of a symmetric group has a unique presentation as a product of some powers of the OGS, un a specific given order. The same paper has demonstrated a strong connection between the OGS and the standard Coxeter presentation of the symmetric group. The OGS presentation helps us to find the Coxeter length and the descent set of an arbitrary element of the symmetric group. Therefore, it motivates us to generalize the OGS for the alternating subgroup of the symmetric group, which we define in this paper. We generalize also the exchange laws for the alternating subgroup, and we will show some interesting properties of it.

AB - There were defined in the paper of Robert Shwartz [3] OGS for symmetric groups, as an interesting generalization of the basis of finite abelian groups. The definition of OGS states that that every element of a symmetric group has a unique presentation as a product of some powers of the OGS, un a specific given order. The same paper has demonstrated a strong connection between the OGS and the standard Coxeter presentation of the symmetric group. The OGS presentation helps us to find the Coxeter length and the descent set of an arbitrary element of the symmetric group. Therefore, it motivates us to generalize the OGS for the alternating subgroup of the symmetric group, which we define in this paper. We generalize also the exchange laws for the alternating subgroup, and we will show some interesting properties of it.

UR - http://www.scopus.com/inward/record.url?scp=85147958228&partnerID=8YFLogxK

U2 - 10.26351/FDE/26/1-2/7

DO - 10.26351/FDE/26/1-2/7

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AN - SCOPUS:85147958228

SN - 0793-1786

VL - 26

SP - 125

EP - 135

JO - Functional Differential Equations

JF - Functional Differential Equations

IS - 1-2

ER -