Menon-type identities derived from actions of subgroups of general linear groups

Yan Li; Daeyeoul Kim

doi:10.1016/j.jnt.2017.03.016

Menon-type identities derived from actions of subgroups of general linear groups

Yan Li
, Daeyeoul Kim^*

^*Corresponding author for this work

Department of Mathematics

China Agricultural University
National Institute for Mathematical Sciences

Research output: Contribution to journal › Journal article › peer-review

20 Scopus citations

Abstract

In this article, we consider the actions of subgroups of the general linear group GL_r(Z_n) on Z_n ^r, including groups of upper triangular matrices in GL_r(Z_n), unipotent groups, Heisenberg groups and extended Heisenberg groups. By applying the Cauchy–Frobenius–Burnside lemma, we obtain several generalizations of the well known Menon's identity.

Original language	English
Pages (from-to)	97-112
Number of pages	16
Journal	Journal of Number Theory
Volume	179
DOIs	https://doi.org/10.1016/j.jnt.2017.03.016
State	Published - 2017.10

Keywords

Cauchy–Frobenius–Burnside lemma
Dirichlet convolution
Heisenberg group
Jordan's totient function
Menon's identity
Unipotent group

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10.1016/j.jnt.2017.03.016

Cite this

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title = "Menon-type identities derived from actions of subgroups of general linear groups",

abstract = "In this article, we consider the actions of subgroups of the general linear group GLr(Zn) on Zn r, including groups of upper triangular matrices in GLr(Zn), unipotent groups, Heisenberg groups and extended Heisenberg groups. By applying the Cauchy–Frobenius–Burnside lemma, we obtain several generalizations of the well known Menon's identity.",

keywords = "Cauchy–Frobenius–Burnside lemma, Dirichlet convolution, Heisenberg group, Jordan's totient function, Menon's identity, Unipotent group",

author = "Yan Li and Daeyeoul Kim",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = oct,

doi = "10.1016/j.jnt.2017.03.016",

language = "English",

volume = "179",

pages = "97--112",

journal = "Journal of Number Theory",

issn = "0022-314X",

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T1 - Menon-type identities derived from actions of subgroups of general linear groups

AU - Li, Yan

AU - Kim, Daeyeoul

PY - 2017/10

Y1 - 2017/10

N2 - In this article, we consider the actions of subgroups of the general linear group GLr(Zn) on Zn r, including groups of upper triangular matrices in GLr(Zn), unipotent groups, Heisenberg groups and extended Heisenberg groups. By applying the Cauchy–Frobenius–Burnside lemma, we obtain several generalizations of the well known Menon's identity.

AB - In this article, we consider the actions of subgroups of the general linear group GLr(Zn) on Zn r, including groups of upper triangular matrices in GLr(Zn), unipotent groups, Heisenberg groups and extended Heisenberg groups. By applying the Cauchy–Frobenius–Burnside lemma, we obtain several generalizations of the well known Menon's identity.

KW - Cauchy–Frobenius–Burnside lemma

KW - Dirichlet convolution

KW - Heisenberg group

KW - Jordan's totient function

KW - Menon's identity

KW - Unipotent group

UR - https://www.scopus.com/pages/publications/85019478709

U2 - 10.1016/j.jnt.2017.03.016

DO - 10.1016/j.jnt.2017.03.016

M3 - Journal article

AN - SCOPUS:85019478709

SN - 0022-314X

VL - 179

SP - 97

EP - 112

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Menon-type identities derived from actions of subgroups of general linear groups

Abstract

Keywords

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