In this chapter, we will introduce the notions of cycles and, in particular, transpositions, which are important elements of the symmetric group. These will help us to understand the group. We will also construct a subgroup of the symmetric group called the alternating group. If \\(n\\ge ...
We investigate the endotrivial modules for the Schur covers of the symmetric and alternating groups and determine the structure of their group of endotrivial modules in all characteristics. We provide a full description of this group by generators and relations in all cases....
Subgroups of symmetric and alternating groups. We show that the Sylow p -subgroups of a symmetric group, respectively an alternating group, are characterized as the p -subgroups containing all elementary abelian p -subgroups up to conjugacy of the symmetric group, respectively the a... JG Berkovi...
On Aschbacher's definition, a subgroup N of a finite group GG is called a pp -superlocal for a prime pp if N = NG ( Op ( N ) )N = N_G \left( {O_p \left( N \right)} \right) . We describe the pp -superlocals in symmetric and alternating groups, thereby resolving part ...
Thisworkisconcernedwithsomebasicrandomwalksonthesymmetricgroup, S n ,andthealternatinggroup,A n .Specifically,weareinterestedinthefollowing models:(a)Randomtranspositionandtransposetopwithrandom;(b)walks generatedbytheuniformmeasureonaconjugacyclass,e.g.,4-cyclesork ...
Subgroups of symmetric and alternating groups. We show that the Sylow p -subgroups of a symmetric group, respectively an alternating group, are characterized as the p -subgroups containing all elementary abelian p -subgroups up to conjugacy of the symmetric group, respectively the a... JG Berkovi...
摘要: We construct explicit generating sets and of the alternating and the symmetric groups, which turn the Cayley graphs and into a family of bounded degree expanders for all sufficiently large . These expanders have many applications in the theory of random walks on group...
Those permutations which leave the product unaltered constitute a group of order n!/2, which is called the alternating group of degree n; it is a self-conjugate subgroup of the symmetric group. From Project Gutenberg In general, if the equation is given arbitrarily, the group will be the sy...
this article, we determine the irreducible projective representations of the symmetric group S d and the alternating group A d over an algebraically closed... J Brundan,A Kleshchev - 《Mathematische Zeitschrift》 被引量: 129发表: 2002年 Characters of projective representations of symmetric groups ...
A base of a permutation group G on a set is a subset B of such that the pointwise stabilizer of B in G is trivial. The base size of G, denoted by b(G), is the minimal cardinality of a base. Let G = Sn or An acting primitively on a set with point stabilizer H. In this no...