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

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

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.

scholarly journals Weights of Partitions and Character Zeros

10.37236/1862 ◽  
2004 ◽  
Vol 11 (2) ◽  
Author(s):  
Christine Bessenrodt ◽  
Jørn B. Olsson
Keyword(s):  
Irreducible Character ◽  
Prime Order ◽  
Alternating Groups ◽  
Non Linear

We classify partitions which are of maximal $p$-weight for all odd primes $p$. As a consequence, we show that any non-linear irreducible character of the symmetric and alternating groups vanishes on some element of prime order.

On the generating graphs of symmetric groups

2018 ◽  
Vol 21 (4) ◽  
pp. 629-649 ◽  
Author(s):  
Fuat Erdem
Keyword(s):  
Symmetric Groups ◽  
Alternating Groups

AbstractLet {S_{n}} and {A_{n}} be the symmetric and alternating groups of degree n, respectively. Breuer, Guralnick, Lucchini, Maróti and Nagy proved that the generating graphs {\Gamma(S_{n})} and {\Gamma(A_{n})} are Hamiltonian for sufficiently large n. However, their proof provided no information as to how large n needs to be. We prove that the graphs {\Gamma(S_{n})} and {\Gamma(A_{n})} are Hamiltonian provided that {n\geq 107}.

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