Sporadic Simple Groups

2002 ◽  
pp. 325-326
Author(s):  
Christopher Parker ◽  
Peter Rowley
Keyword(s):  
Simple Groups ◽  
Sporadic Simple Groups

scholarly journals Commuting involution graphs for sporadic simple groups

2007 ◽  
Vol 316 (2) ◽  
pp. 849-868 ◽  
Author(s):  
C. Bates ◽  
D. Bundy ◽  
S. Hart ◽  
P. Rowley
Keyword(s):  
Simple Groups ◽  
Sporadic Simple Groups

scholarly journals On the Structure of Integral Group Rings of Sporadic Groups

2000 ◽  
Vol 3 ◽  
pp. 274-306 ◽  
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.

scholarly journals Pointed Hopf algebras over the sporadic simple groups

2011 ◽  
Vol 325 (1) ◽  
pp. 305-320 ◽  
Author(s):  
N. Andruskiewitsch ◽  
F. Fantino ◽  
M. Graña ◽  
L. Vendramin
Keyword(s):  
Hopf Algebras ◽  
Simple Groups ◽  
Pointed Hopf Algebras ◽  
Sporadic Simple Groups

Amalgams of minimal local subgroups and sporadic simple groups

2010 ◽  
pp. 495-506
Author(s):  
C W Parker ◽  
P Rowley ◽  
C. M. Campbell ◽  
E. F. Robertson ◽  
T. C. Hurley ◽  
...  
Keyword(s):  
Simple Groups ◽  
Sporadic Simple Groups

scholarly journals An identification theorem for the sporadic simple groups F2 and M(23)

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Chris Parker ◽  
Gernot Stroth
Keyword(s):  
Simple Groups ◽  
Sporadic Groups ◽  
Sporadic Simple Groups ◽  
Identification Theorem

Abstract.We identify the sporadic groups M(23) and F

scholarly journals Amalgams Determined By Locally Projective Actions

2004 ◽  
Vol 176 ◽  
pp. 19-98 ◽  
Author(s):  
A. A. Ivanov ◽  
S. V. Shpectorov
Keyword(s):  
Linear Group ◽  
Infinite Series ◽  
Connected Graph ◽  
Interesting Case ◽  
Simple Groups ◽  
Transitive Action ◽  
Sporadic Simple Groups ◽  
Global Stabilizer

AbstractA locally projective amalgam is formed by the stabilizer G(x) of a vertex x and the global stabilizer G{x, y} of an edge (containing x) in a group G, acting faithfully and locally finitely on a connected graph Γ of valency 2n - 1 so that (i) the action is 2-arc-transitive; (ii) the subconstituent G(x)Γ(x) is the linear group SLn(2) = Ln(2) in its natural doubly transitive action and (iii) [t, G{x, y}] < O2(G(x) n G{x, y}) for some t G G{x, y} \ G(x). D. Z. Djokovic and G. L. Miller [DM80], used the classical Tutte’s theorem [Tu47], to show that there are seven locally projective amalgams for n = 2. Here we use the most difficult and interesting case of Trofimov’s theorem [Tr01] to extend the classification to the case n > 3. We show that besides two infinite series of locally projective amalgams (embedded into the groups AGLn(2) and O2n+(2)) there are exactly twelve exceptional ones. Some of the exceptional amalgams are embedded into sporadic simple groups M22, M23, Co2, J4 and BM. For each of the exceptional amalgam n = 3, 4 or 5.

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