Invariable generation of the symmetric group
نویسندگان
چکیده
منابع مشابه
Invariable Generation of the Symmetric Group
Abstract. We say that permutations π1, . . . , πr ∈ Sn invariably generate Sn if, no matter how one chooses conjugates π 1 , . . . , π r of these permutations, π 1 , . . . , π r generate Sn. We show that if π1, π2, π3 are chosen randomly from Sn then, with probability tending to 1 as n → ∞, they do not invariably generate Sn. By contrast it was shown recently by Pemantle, Peres and Rivin that f...
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Let $G$ be a finite group and $Gamma(G)$ the prime graph of $G$. Recently people have been using prime graphs to study simple groups. Naturally we pose a question: can we use prime graphs to study almost simple groups or non-simple groups? In this paper some results in this respect are obtained and as follows: $Gcong S_p$ if and only if $|G|=|S_p|$ and $Gamma(G)=Gamma(S_p)$, whe...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2017
ISSN: 0012-7094
DOI: 10.1215/00127094-0000007x