Recognition of alternating groups of prime degree from their element orders

2000 ◽  
Vol 41 (2) ◽  
pp. 294-302 ◽  
Author(s):  
A. S. Kondrat'ev ◽  
V. D. Mazurov
Keyword(s):  
Element Orders ◽  
Alternating Groups ◽  
Prime Degree

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

NSE characterization of some alternating groups

2014 ◽  
Vol 14 (02) ◽  
pp. 1550012
Author(s):  
Neda Ahanjideh ◽  
Bahareh Asadian
Keyword(s):  
Finite Group ◽  
Element Orders ◽  
Alternating Groups ◽  
Set Of Element Orders ◽  
A Finite Group

Let p ≥ 5 be a prime and n ∈ {p, p + 1, p + 2}. Let G be a finite group and πe(G) be the set of element orders of G. Assume that k ∈ πe(G) and mk(G) is the number of elements of order k in G. Set nse (G) = {mk(G) : k ∈ πe(G)}. In this paper, we show that if nse (An) = nse (G), p ∈ π(G) and p2 ∤ |G|, then G ≅ An. As a consequence of our result, we show that if nse (An) = nse (G) and |G| = |An|, then G ≅ An.

scholarly journals Conjugacy Classes ofP-Cycles of Type D in Alternating Groups

2014 ◽  
Vol 42 (10) ◽  
pp. 4426-4434 ◽  
Author(s):  
Fernando Fantino
Keyword(s):  
Conjugacy Classes ◽  
Alternating Groups ◽  
Type D

On correspondence between orders and ideals with a normal basis in cyclic subfields of Q(ξp) of a prime degree l

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Juraj Kostra
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Normal Basis ◽  
Prime Degree ◽  
One To One

AbstractLet K be a tamely ramified cyclic algebraic number field of prime degree l. In the paper one-to-one correspondence between all orders of K with a normal basis and all ideals of K with a normal basis is given.

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

Finite Groups with Nonmonomial Characters of Prime Degree

2003 ◽  
Vol 74 (5/6) ◽  
pp. 671-675 ◽  
Author(s):  
I. A. Sagirov
Keyword(s):  
Finite Groups ◽  
Prime Degree

scholarly journals Covering the alternating groups by products of cycle classes

2008 ◽  
Vol 115 (7) ◽  
pp. 1235-1245 ◽  
Author(s):  
Marcel Herzog ◽  
Gil Kaplan ◽  
Arieh Lev
Keyword(s):  
Alternating Groups ◽  
By Products ◽  
Cycle Classes
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