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Marius Tùarnùauceanu (2018)
A note on the product of element orders of finite abelian groups
Jafarian Amiri, S. Majid (2013)
Characterization of $A_5$ and $PSL(2,7)$ by sum of element ordersInternational Journal of Group Theory, 2
S. Amiri, J. Moori (2013)
MAXIMUM SUM ELEMENT ORDERS OF ALL PROPER SUBGROUPS OF PGL(2;q)Bulletin of The Iranian Mathematical Society, 39
S. Amiri (2013)
Second Maximum Sum of Element Orders of Finite Nilpotent GroupsCommunications in Algebra, 41
H. Amiri, S. Amiri, I. Isaacs (2009)
Sums of Element Orders in Finite GroupsCommunications in Algebra, 37
A. Lubotzky, D. Segal (2003)
Finite Group Theory
S. Amiri, M. Amiri (2014)
Second maximum sum of element orders on finite groupsJournal of Pure and Applied Algebra, 218
Given a finite group G, we denote by $$\psi (G)$$ ψ ( G ) the sum of the element orders in G. In this article, we prove that if t is the number of nonidentity conjugacy classes in G, then $$\psi (G)=1+t|G|$$ ψ ( G ) = 1 + t | G | if and only if G is either a group of prime order or a nonabelian group of the square-free order with two prime divisors. Also we find a unique group with the second maximum sum of the element orders among all finite groups of the same square-free order.
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: May 2, 2016
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