منابع مشابه
Local Fusion Graphs for Symmetric Groups
For a group G, π a set of odd positive integers and X a set of involutions of G we define a graph Fπ(G,X). This graph, called a π-local fusion graph, has vertex set X with x, y ∈ X joined by an edge provided x 6= y and the order of xy is in π. In this paper we investigate Fπ(G,X) when G is a finite symmetric group for various choices of X and π.
متن کاملLocal Fusion Graphs and Sporadic Simple Groups
For a group G with G-conjugacy class of involutions X, the local fusion graph F(G,X) has X as its vertex set, with distinct vertices x and y joined by an edge if, and only if, the product xy has odd order. Here we show that, with only three possible exceptions, for all pairs (G,X) with G a sporadic simple group or the automorphism group of a sporadic simple group, F(G,X) has diameter 2.
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.
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We construct explicit generating sets Sn and S̃n of the alternating and the symmetric groups, which turn the Cayley graphs C(Alt(n), Sn) and C(Sym(n), S̃n) into a family of bounded degree expanders for all n. This answers affirmatively an old question which has been asked many times in the literature. These expanders have many applications in the theory of random walks on groups, card shuffling a...
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Let r be finite connected and G a group of automorphisms of r which is transitive on vertices. Suppose that, for a vertex 0 of r, S ~ G~(O') ::; Aut S for some simple group S with S acting primitively on the set r( a) of neighbours of 0, and suppose that G is minimal with these properties. Then one of: (i) G is a nonabelian simple group, (ii) r is a Cayley graph for a normal subgroup N of G and...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2013
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt-2012-0027