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1.
In this paper we prove that if G is a finite exceptional simple group of Lie type, then G admits a 2-covering if, and only if, it is one of the following groups: ${G_2(2^{a}), F_4(3^{a}), G_2(2)', ^{2}G_2(3)', ^{2}F_4(2)'}$ G 2 ( 2 a ) , F 4 ( 3 a ) , G 2 ( 2 ) ′ , 2 G 2 ( 3 ) ′ , 2 F 4 ( 2 ) ′ . Furthermore, if G is a finite sporadic simple group, then G admits a 2-covering if, and only if, G = M11.  相似文献   

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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) ⩽ 7, with equality if and only if G is the Mathieu group M24 in its natural action on 24 points. This settles a conjecture of Cameron.  相似文献   

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LetVbeavectorspaceoverfieldK=GF(q),whereq=2",nodd.ThethereexistsinGL(V)somesubgroupH,whichisisomorphictoSz(q),andtheactionofHonVderivessomeirreduciblemodulestructureforH-LetF=GF(2),thenVcanbeseenasanFH-mod-ule,Vremainsirreducible,andVissaidtobeanaturalFH-module.Thenotionofnaturalmodule'forSz(q)canbegeneralizedtothewrethproductSz(q)wed(thedefinitionforthewreathproduct,seeLlj'9'l9),Thenotationsandterminol-ogyinthispaper'exceptforfewexceptions,areeitherstandardoeasiluaccessiblefromL2j'…  相似文献   

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We show that each sporadic simple group G can be uniquely determined by the set of the orders of the maximal abelian subgroups of G.  相似文献   

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We obtain efficient programs for obtaining representatives of all the conjugacy classes of all the sporadic simple groups except the Monster and the Baby Monster.  相似文献   

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In 1955 Hall and Paige conjectured that a finite group is admissible, i.e., admits complete mappings, if its Sylow 2-subgroup is trivial or noncyclic. In a recent paper, Wilcox proved that any minimal counterexample to this conjecture must be simple, and further, must be either the Tits group or a sporadic simple group. In this paper we improve on this result by proving that the fourth Janko group is the only possible minimal counterexample to this conjecture: John Bray reports having proved that this group is also not a counterexample, thus completing a proof of the Hall–Paige conjecture.  相似文献   

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We consider 2-local geometries and other subgroup complexes for sporadic simple groups. For six groups, the fixed point set of a noncentral involution is shown to be equivariantly homotopy equivalent to a standard geometry for the component of the centralizer. For odd primes, fixed point sets are computed for sporadic groups having an extraspecial Sylow p-subgroup of order p3, acting on the complex of those p-radical subgroups containing a p-central element in their centers. Vertices for summands of the associated reduced Lefschetz modules are described.  相似文献   

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LetG be a finite sporadic simple group. Then there exist groupsn.G., n.G.2 and, in casen is even,n.G.2i, the group isoclinic to but not isomorphic ton.G.2. The Schur indices of all irreducible characters of these groups are computed. In a previous paper this was done for the groupsn.G (with one exception). The division algebra corresponding to a character is determined by all the local Schur indices. These are all listed in the tables in Section 6 using the notation from the ATLAS.  相似文献   

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This work has been supported by the Deutsche Forschungsgemeinschaft and Carleton University, Ottawa.  相似文献   

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In this paper we completely characterise irreducible tensor products of a basic spin module with an irreducible module for alternating groups in characteristic 2. This completes the classification of irreducible tensor products of representations of alternating groups.  相似文献   

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In this paper we give details of the proofs performed with GAP of the theorems of our paper [N. Andruskiewitsch, F. Fantino, M. Graña, L. Vendramin, Pointed Hopf algebras over the sporadic simple groups, J. Algebra 325 (1) (2011) 305–320].  相似文献   

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