منابع مشابه
Semi-Presentations for the Sporadic Simple Groups
A semi-presentation for a group G is a set of relations which characterises a set of generators of G up to automorphism. We discuss some techniques for finding semi-presentations and illustrate them by exhibiting semi-presentations on standard generators for the 26 sporadic simple groups and their automorphism groups. We then show how these semipresentations were used to check the data in the 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 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 کاملSchur Multipliers of the Known Finite Simple Groups
In this note, we announce some results about the Schur multipliers of the known finite simple groups. Proofs will appear elsewhere. We shall conclude with a summary of current knowledge on the subject. Basic properties of multipliers and covering groups of finite groups are discussed in [6]. Notation for groups of Lie type is standard [3], [8]. G' denotes the commutator subgroup of the group G,...
متن کاملReduction of the Hall-paige Conjecture to Sporadic Simple Groups
A complete mapping of a group G is a permutation φ : G → G such that g 7→ gφ(g) is also a permutation. Hall and Paige proved that a finite group admits a complete mapping only if its Sylow-2 subgroup is trivial or non-cyclic. They conjectured that this condition is also sufficient. We prove that it is sufficient to check the conjecture for the 27 sporadic simple groups.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1979
ISSN: 0021-8693
DOI: 10.1016/0021-8693(79)90177-7