NEW CRITERIA FOR SOLVABILITY, NILPOTENCY AND OTHER PROPERTIES OF FINITE GROUPS IN TERMS OF THE ORDER ELEMENTS OR SUBGROUPS
. In this survey we shall describe some recent criteria for solvability, nilpotency and other properties of finite groups G , based either on the orders of the elements of G or on the orders of the…
On the sum of the inverses of the element orders in finite groups
- MathematicsCommunications in Algebra
Abstract Let G be a finite group. Recently various functions are defined related to the set of order elements of G and using these functions, some interesting criteria for solvability, nilpotency,…
The solvability of a finite group by the sum of powers of element orders
We prove a new criterion for the solvability of the ﬁnite groups, depending on the function ψ k ( G ) which is deﬁned as the sum of k -th powers of the element orders of G . We show that our result…
SHOWING 1-10 OF 46 REFERENCES
Atlas of finite groups : maximal subgroups and ordinary characters for simple groups
This atlas covers groups from the families of the classification of finite simple groups. Recently updated incorporating corrections
ON THE SUM OF ELEMENT ORDERS OF FINITE ABELIAN GROUPS
Abstract In this note some properties of the sum of element orders of a finite abelian group are studied.
Sums of Element Orders in Finite Groups
Given a finite group G, write ψ(G) to denote the sum of the orders of the elements of G. Our main result is that if C is a cyclic group and G is a noncyclic group of the same order, then ψ(G) < ψ(C).
On the character degree sums
ABSTRACT Let G be a finite group, and T(G) be the sum of all complex irreducible character degrees of G. In this paper, we get the exact lower bound of |G|∕T(G) for a non-r-solvable group G.
ON THE SUM OF ELEMENT ORDERS OF FINITE SIMPLE GROUPS
Let G be a finite group and ψ(G) = ∑g∈Go(g), where o(g) denotes the order of g ∈ G. In this short paper we show that the conjecture of minimality of ψ(G) in simple groups, posed in [J. Algebra Appl.…
Sum of Element Orders of Maximal Subgroups of the Symmetric Group
For a finite group G, let ψ(G) denote the sum of element orders of G. The aim of this article is to show that ψ(H) < ψ(A n ) for every proper subgroup H of the symmetric group of degree n, which is…
ON THE NUMBER OF PRIME ORDER SUBGROUPS OF FINITE GROUPS
- MathematicsJournal of the Australian Mathematical Society
Abstract Let G be a finite group and let δ(G) be the number of prime order subgroups of G. We determine the groups G with the property δ(G)≥∣G∣/2−1, extending earlier work of C. T. C. Wall, and we…
The Characterization of PSL(2, q) by Its Element Orders
Abstract We show that the simple groups PSL(2, q), q ≠ 9, are characterized by their element orders.
SUM OF ELEMENT ORDERS ON FINITE GROUPS OF THE SAME ORDER
For a finite group G, let ψ(G) denote the sum of element orders of G. It is known that the maximum value of ψ on the set of groups of order n, where n is a positive integer, will occur at the cyclic…
Second Maximum Sum of Element Orders of Finite Nilpotent Groups
In , the authors proved that the maximum sum of element orders on finite groups of the same order occurs in cyclic group. In this paper we obtain the structure of groups having maximum sum of…