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 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

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 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

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

On second degree cohomology of symmetric and alternating groups

1993 ◽  
Vol 21 (2) ◽  
pp. 583-600 ◽  
Author(s):  
Alexander S. Kleshchev ◽  
Alexander A. Premet
Keyword(s):  
Alternating Groups ◽  
Second Degree

scholarly journals On types of matrices and centralizers of matrices and permutations

2014 ◽  
Vol 17 (5) ◽  
Author(s):  
John R. Britnell ◽  
Mark Wildon
Keyword(s):  
Finite Field ◽  
Alternating Groups ◽  
Type Invariant ◽  
The Matrix ◽  
Generalized Type

AbstractIt is known that the centralizer of a matrix over a finite field depends, up to conjugacy, only on the type of the matrix, in the sense defined by J. A. Green. In this paper an analogue of the type invariant is defined that in general captures more information; using this invariant the result on centralizers is extended to arbitrary fields. The converse is also proved: thus two matrices have conjugate centralizers if and only if they have the same generalized type. The paper ends with the analogous results for symmetric and alternating groups.

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