منابع مشابه
On base sizes for symmetric groups
A base of a permutation group G on a set Ω is a subset B of Ω 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 note we prove that if H acts primitively on {1, . . . , n}, and does not contain An, then b(G) = 2 for all n ≥ 13. Combined w...
متن کاملBase sizes for sporadic simple groups
Let G be a permutation group acting on a set Ω. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. We write b(G) for the minimal size of a base for G. We determine the precise value of b(G) for every primitive almost simple sporadic group G, with the exception of two cases involving the Baby Monster group. As a corollary, we deduce that b(G) 6 7, with equality if and onl...
متن کاملBase sizes for simple groups and a conjecture of Cameron
Let G be a permutation group on a finite set Ω. A base for G is a subset B ⊆ Ω with pointwise stabilizer in G that is trivial; we write b(G) for the smallest size of a base for G. In this paper we prove that b(G) ! 6 if G is an almost simple group of exceptional Lie type and Ω is a primitive faithful G-set. An important consequence of this result, when combined with other recent work, is that b...
متن کاملOn Coprimality Graphs for Symmetric Groups
For G a group, X a subset of G and π a set of positive integers we define a graph Cπ(G,X) whose vertex set is X with x, y ∈ X joined by an edge provided x 6= y and the order of xy is in π. Here we investigate Cπ(G,X) when G is a finite symmetric group and X is a G-conjugacy class of elements of order p, p a prime.
متن کاملOn the decomposition map for symmetric groups
Let R be the Z-module generated by the irreducible characters of the symmetric group Sd . We determine bases for the kernel of the decomposition map. It is known that R ⊗Z F is isomorphic to the radical quotient of the Solomon descent algebra when F is a field of characteristic zero. We show that when F has prime characteristic and I d br is the kernel of the decomposition map for prime p then ...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2011
ISSN: 0024-6093
DOI: 10.1112/blms/bdq123