Cascade Synthesis of a Class of Two Element Orders Fractional Immittance Functions

2021 ◽  
Author(s):  
Guishu Liang ◽  
Andong Zhou
Keyword(s):  
Element Orders

scholarly journals Large element orders and the characteristic of Lie-type simple groups

2009 ◽  
Vol 322 (3) ◽  
pp. 802-832 ◽  
Author(s):  
William M. Kantor ◽  
Ákos Seress
Keyword(s):  
Simple Groups ◽  
Large Element ◽  
Element Orders

Element orders in coverings of symmetric and alternating groups

1999 ◽  
Vol 38 (3) ◽  
pp. 159-170 ◽  
Author(s):  
A. V. Zavarnitsin ◽  
V. D. Mazurov
Keyword(s):  
Element Orders ◽  
Alternating Groups

Recognition by Spectrum of L16(2m)

2007 ◽  
Vol 14 (04) ◽  
pp. 585-591 ◽  
Author(s):  
Maria A. Grechkoseeva ◽  
Wujie Shi ◽  
Andrey V. Vasilev
Keyword(s):  
Linear Groups ◽  
Recognition By Spectrum ◽  
Element Orders ◽  
Characteristic 2

In this paper we prove that the simple linear groups L16(2m)(m ≥ 1) over fields of characteristic 2 are recognizable by the sets of their element orders.

scholarly journals A criterion for solvability of a finite group by the sum of element orders

2018 ◽  
Vol 516 ◽  
pp. 115-124 ◽  
Author(s):  
Morteza Baniasad Azad ◽  
Behrooz Khosravi
Keyword(s):  
Finite Group ◽  
Element Orders ◽  
A Finite Group

Sums of element orders in groups of order 2m with m odd

2019 ◽  
Vol 47 (5) ◽  
pp. 2035-2048 ◽  
Author(s):  
Marcel Herzog ◽  
Patrizia Longobardi ◽  
Mercede Maj
Keyword(s):  
Element Orders

scholarly journals The second maximal groups with respect to the sum of element orders

2021 ◽  
Vol 225 (3) ◽  
pp. 106531 ◽  
Author(s):  
Marcel Herzog ◽  
Patrizia Longobardi ◽  
Mercede Maj
Keyword(s):  
Element Orders

Variations on results on orders of products in finite groups

2020 ◽  
pp. 1-7
Author(s):  
Juan Martínez ◽  
Alexander Moretó
Keyword(s):  
Finite Groups ◽  
Prime Power ◽  
Simple Groups ◽  
Prime Power Order ◽  
Finite Simple Groups ◽  
Prime Divisors ◽  
Element Orders ◽  
Hall Subgroups ◽  
A Finite Group

In 2014, Baumslag and Wiegold proved that a finite group G is nilpotent if and only if o(xy) = o(x)o(y) for every x, y ∈ G with (o(x), o(y)) = 1. This has led to a number of results that characterize the nilpotence of a group (or the existence of nilpotent Hall subgroups, or the existence of normal Hall subgroups) in terms of prime divisors of element orders. Here, we look at these results with a new twist. The first of our main results asserts that G is nilpotent if and only if o(xy) ⩽ o(x)o(y) for every x, y ∈ G of prime power order with (o(x), o(y)) = 1. As an immediate consequence, we recover the Baumslag–Wiegold theorem. The proof of this result is elementary. We prove some variations of this result that depend on the classification of finite simple groups.

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