Simple Bψ-groups

In a finite group G , ψ ( G ) denotes the sum of element orders of G . A finite group G is said to be a B ψ -group if ψ ( H ) < | G | for any proper subgroup H of G . In Lazorec (Rev Real Acad Cienc Exact Fis Nat Ser A Mat 117:448, 2023), Lazorec put forward the following question: Question. What...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2024, Vol.118 (3)
Main Author: Baniasad Azad, Morteza
Format: Article
Language:English
Subjects:
Applications of Mathematics
Group theory
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Questions
Subgroups
Theoretical
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Summary:In a finite group G , ψ ( G ) denotes the sum of element orders of G . A finite group G is said to be a B ψ -group if ψ ( H ) < | G | for any proper subgroup H of G . In Lazorec (Rev Real Acad Cienc Exact Fis Nat Ser A Mat 117:448, 2023), Lazorec put forward the following question: Question. What can be said about the B ψ property of the finite simple groups PSL ( 2 , q ) ? In this paper, we show that if S is a finite simple group, such that S ≠ A l t ( n ) for any n ≥ 14 , then S is a B ψ -group.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-024-01631-x