Detecting structural properties of finite groups by the sum of element orders
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DOI: 10.1007/s11856-020-2033-9
Abstract: In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable… read more here.
Keywords: finite groups; detecting structural; structural properties; sum element ... See more keywords
Sum of the Element Orders in Groups of the Square-Free Orders
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DOI: 10.1007/s40840-016-0353-z
Abstract: 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,… read more here.
Keywords: sum element; element orders; group; groups square ... See more keywords
On a Divisibility Property Involving the Sum of Element Orders
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DOI: 10.1007/s40840-020-00987-8
Abstract: A finite group G is called $$\psi $$ ψ -divisible if $$\psi (H)|\psi (G)$$ ψ ( H ) | ψ ( G ) for any subgroup H of G , where $$\psi (H)$$ ψ (… read more here.
Keywords: sum element; psi; element orders; divisibility property ... See more keywords