The characterization of some cyclic groups by the product of element orders

被引：1

作者：

Shafiei, Hamed ^{[1
]}

Khosravi, Behrooz ^{[1
]}

Azad, Morteza Baniasad ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Pure Math, 424 Hafez Ave, Tehran 15914, Iran

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2023年

关键词：

Finite groups; simple group; element orders; product of element orders;

D O I：

10.1142/S0219498824500919

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a finite group. We denote by psi '(G) the integer Pi(g is an element of G)o(g), where o(g) denotes the order of g is an element of G. It is verified that some finite groups are uniquely determined by their orders and their product of element orders. In this paper, we prove that, if p, q, r, t are different prime numbers, then Z(p3), Z(pq), Z(p2q) and Z(pqrt) are characterized by psi '(G) and if psi '(G) = psi '(Z(pqr)), then G congruent to A(5) or Z(pqr).

引用

页数：9

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