Generating alternating groups
نویسندگان
چکیده
منابع مشابه
Generating Symmetric and Alternating Groups with Elements of Fixed Order
Many of the commonly-used generating sets for the symmetric group Σn and the alternating group An either consist of a number of generators that grows as n grows or else contain an element whose order grows as n grows. For instance, Σn is generated by the set of adjacent transpositions, and it is also generated by a single transposition along with an n-cycle. Similarly, An is generated by all 3-...
متن کاملAsymptotics of Generating the Symmetric and Alternating Groups
The probability that a random pair of elements from the alternating group An generates all of An is shown to have an asymptotic expansion of the form 1¡1/n¡ 1/n2¡4/n3¡23/n4¡171/n5¡ ... . This same asymptotic expansion is valid for the probability that a random pair of elements from the symmetric group Sn generates either An or Sn. Similar results hold for the case of r generators (r > 2). MSC 2...
متن کاملAlternating subgroups of Coxeter groups
We study combinatorial properties of the alternating subgroup of a Coxeter group, using a presentation of it due to Bourbaki.
متن کاملPermutation Generators of Alternating Groups
using elementary permutations also called modules These modules have a simple structure and are based on internal smaller permutations Two cases are considered In the rst the modules apply internal permutations only It has been proved that the composition of modules generates the alternating group for the number of binary inputs bigger than In the second DES like modules are considered and it i...
متن کاملFrobenius Classes in Alternating Groups
We present a method, based on an old idea of Serre, for completely computing Frobenius classes in alternating groups. We contrast this method with other approaches in examples involving the alternating groups A3 and A9. The method can be useful for proper subgroups of alternating groups as well, and we present examples involving the 168-element group PSL2(7) = GL3(2) and the Mathieu group M24.
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ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 1997
ISSN: 0385-4035
DOI: 10.14492/hokmj/1351257975