Characteristic classes and 2—modular representations for some sporadic simple groups — II

In this paper we conduct a systematic computerized search for groups generated by small, but highly symmetric, sets of elements of order 3. Many classical groups are readily obtained in this way, as are a number of sporadic simple groups. Firstly, we introduce monomial modular representations as these will prove useful later in the paper. Then the techniques of symmetric generation developed elsewhere are described afresh. The results we obtain are presented in a convenient tabular form, together with relevant character tables.

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On the existence and uniqueness of the sporadic simple groups J2 and J3 of Z. Janko

Journal of Group Theory ◽

10.1515/jgth.2001.019 ◽

2001 ◽

Vol 4 (2) ◽

Author(s):

Wolfgang Lempken

Keyword(s):

Existence And Uniqueness ◽

Simple Groups ◽

Sporadic Simple Groups

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Commuting involution graphs for sporadic simple groups

Journal of Algebra ◽

10.1016/j.jalgebra.2007.04.019 ◽

2007 ◽

Vol 316 (2) ◽

pp. 849-868 ◽

Cited By ~ 13

Author(s):

C. Bates ◽

D. Bundy ◽

S. Hart ◽

P. Rowley

Keyword(s):

Simple Groups ◽

Sporadic Simple Groups

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On the Structure of Integral Group Rings of Sporadic Groups

LMS Journal of Computation and Mathematics ◽

10.1112/s1461157000000309 ◽

2000 ◽

Vol 3 ◽

pp. 274-306 ◽

Cited By ~ 6

Author(s):

Frauke M. Bleher ◽

Wolfgang Kimmerle

Keyword(s):

Automorphism Groups ◽

Symmetric Groups ◽

Computational Procedure ◽

Isomorphism Problem ◽

Simple Groups ◽

Group Rings ◽

Integral Group ◽

Sporadic Groups ◽

Integral Group Rings ◽

Sporadic Simple Groups

AbstractThe object of this article is to examine a conjecture of Zassenhaus and certain variations of it for integral group rings of sporadic groups. We prove the ℚ-variation and the Sylow variation for all sporadic groups and their automorphism groups. The Zassenhaus conjecture is established for eighteen of the sporadic simple groups, and for all automorphism groups of sporadic simple groups G which are different from G. The proofs are given with the aid of the GAP computer algebra program by applying a computational procedure to the ordinary and modular character tables of the groups. It is also shown that the isomorphism problem of integral group rings has a positive answer for certain almost simple groups, in particular for the double covers of the symmetric groups.

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