A representation for the Lyons group in GL 2480 (4), and a new uniqueness proof

1998 ◽  
Vol 70 (1) ◽  
pp. 11-15 ◽  
Author(s):  
Robert A. Wilson
Keyword(s):  
Uniqueness Proof ◽  
Lyons Group

Another existence and uniqueness proof for McLaughlin's simple group

2003 ◽  
Vol 6 (4) ◽  
Author(s):  
Mathias Kratzer ◽  
Wolfgang Lempken ◽  
Gerhard O. Michler ◽  
Katsushi Waki
Keyword(s):  
Simple Group ◽  
Existence And Uniqueness ◽  
Uniqueness Proof

A uniqueness proof for the Wulff Theorem

1991 ◽  
Vol 119 (1-2) ◽  
pp. 125-136 ◽  
Author(s):  
Irene Fonseca ◽  
Stefan Müller
Keyword(s):  
Measure Theory ◽  
Isoperimetric Problem ◽  
Geometric Measure Theory ◽  
Minkowski Inequality ◽  
Main Ingredient ◽  
Anisotropic Surface ◽  
Finite Perimeter ◽  
Uniqueness Proof ◽  
Elastic Crystals ◽  
Anisotropic Surface Energy

SynopsisThe Wulff problem is a generalisation of the isoperimetric problem and is relevant for the equilibrium of (small) elastic crystals. It consists in minimising the (generally anisotropic) surface energy among sets of given volume. A solution of this problem is given by a geometric construction due to Wulff. In the class of sets of finite perimeter this was first shown by J. E. Taylor who, using methods of geometric measure theory, also proved uniqueness. Here a more analytic uniqueness proof is presented. The main ingredient is a sharpened version of the Brunn–Minkowski inequality.

scholarly journals Completing the Brauer Trees for the Sporadic Simple Lyons Group

2002 ◽  
Vol 5 ◽  
pp. 18-33 ◽  
Author(s):  
Jürgen Müller ◽  
Max Neunhöffer ◽  
Frank Röhr ◽  
Robert Wilson
Keyword(s):  
Representation Theory ◽  
Computer Algebra ◽  
Computer Algebra Systems ◽  
Computational Representation ◽  
Lyons Group

AbstractIn this paper, the Brauer trees are completed for the sporadic simple Lyons group Ly in characteristics 37 and 67. The results are obtained using tools from computational representation theory—in particular, a new condensation technique—and with the assistance of the computer algebra systems MeatAxe and GAP.

The maximal subgroups of the Lyons group

1985 ◽  
Vol 97 (3) ◽  
pp. 433-436 ◽  
Author(s):  
Robert A. Wilson
Keyword(s):  
Simple Group ◽  
Maximal Subgroups ◽  
Subgroup Structure ◽  
Image Position ◽  
Lyons Group

In this paper we complete the work begun in [2] on the subgroup structure of the Lyons simple group Ly of order

A New Uniqueness Proof for the Held Group

1991 ◽  
Vol 23 (3) ◽  
pp. 235-238 ◽  
Author(s):  
Leonard H. Soicher
Keyword(s):  
Uniqueness Proof ◽  
Held Group

Another Existence and Uniqueness Proof of the Tits Group

2008 ◽  
Vol 15 (02) ◽  
pp. 241-278
Author(s):  
Gerhard O. Michler ◽  
Lizhong Wang
Keyword(s):  
Finite Groups ◽  
Existence And Uniqueness ◽  
Frobenius Group ◽  
Nilpotency Class ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Uniqueness Proof ◽  
Groups Of Lie Type ◽  
Uniqueness Criteria ◽  
Tits Group

In this article we give a self-contained existence and uniqueness proof for the Tits simple group T. Parrott gave the first uniqueness proof. Whereas Tits' and Parrott's results employ the theory of finite groups of Lie type, our existence and uniqueness proof follows from the general algorithms and uniqueness criteria for abstract finite simple groups described in the first author's book [11]. All we need from the previous papers is the fact that the centralizer H of the Tits group T is an extension of a 2-group J with order 29 and nilpotency class 3 by a Frobenius group F of order 20 such that the center Z(H) has order 2 and any Sylow 5-subgroup Q of H has a centralizer CJ(Q) ≤ Z(H).

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