منابع مشابه
finite simple groups which are the products of symmetric or alternating groups with $l_{3}(4)$
in this paper, we determine the simple groups $g=ab$, where $b$ is isomorphic to $l_{3}(4)$ and $a$ isomorphic to an alternating or a symmetric group on $ngeq5$, letters.
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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...
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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...
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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.
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Hurwitz not only gave an upper bound for the number of automorphisms of a compact Riemann surface of genus greater than 2, but also gave a characterization of which finite groups could be groups of automorphisms achieving this bound. In practice, however, the identification of such groups and of the surfaces they act on is difficult except in special cases. We survey what is known. 1. How I Got...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1991
ISSN: 0021-8693
DOI: 10.1016/0021-8693(91)90115-o