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

被引：20

作者：

Li, Yan ^{[1
]}

Kim, Daeyeoul ^{[2
]}

机构：

[1] China Agr Univ, Dept Appl Math, Beijing 100083, Peoples R China

[2] Natl Inst Math Sci, Yuseong Daero 1689 Gil, Daejeon 305811, South Korea

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 179卷

关键词：

Menon's identity; Dirichlet convolution; Jordan's totient function; Cauchy-Frobenius-Burnside lemma; Unipotent group; Heisenberg group; FINITE DEDEKIND DOMAINS;

D O I：

10.1016/j.jnt.2017.03.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：97 / 112

页数：16

共 15 条

[1] Haukkanen P., 1997, Indian J. Math., V39, P37
[2] Haukkanen P., 2005, AEQUATIONES MATH, V70, P240, DOI DOI 10.1007/S00010-005-2805-7
[3] Menon PKesava, 1965, The Journal of the Indian Mathematical Society, V29, P155
[4] A Menon-type identity in residually finite Dedekind domains
Miguel, C.
[J]. JOURNAL OF NUMBER THEORY, 2016, 164 : 43 - 51
[5] Menon's identity in residually finite Dedekind domains
Miguel, C.
[J]. JOURNAL OF NUMBER THEORY, 2014, 137 : 179 - 185
[6] Nageswara Rao K., 1972, Lecture Notes Math., V251, P181
[7] RAMAIAH VS, 1978, J REINE ANGEW MATH, V303, P265
[8] Rotman Joseph J., 2000, A first course in abstract algebra
[9] On a theorem of Jordan
Serre, JP
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 40 (04): : 429 - 440
[10] Sivaramakrishnan R., 1979, Canad. Math. Bull., V22, P207

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