Automorphisms of fusion systems of finite simple groups of Lie typeandAutomorphisms of fusion systems of sporadic simple groups

2019 ◽  
Vol 262 (1267) ◽  
pp. 0-0
Author(s):  
Carles Broto ◽  
Jesper Møller ◽  
Bob Oliver
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Fusion Systems ◽  
Sporadic Simple Groups

A Characterization of Finite Simple Groups by the Degrees of Vertices of Their Prime Graphs

2005 ◽  
Vol 12 (03) ◽  
pp. 431-442 ◽  
Author(s):  
A. R. Moghaddamfar ◽  
A. R. Zokayi ◽  
M. R. Darafsheh
Keyword(s):  
Finite Group ◽  
Prime Graph ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Natural Numbers ◽  
Prime Graphs ◽  
Sporadic Simple Groups ◽  
A Finite Group ◽  
Groups Of Lie Type

If G is a finite group, we define its prime graph Γ(G) as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, q are joined by an edge, denoted by p~q, if there is an element in G of order pq. Assume [Formula: see text] with primes p1<p2<⋯<pkand natural numbers αi. For p∈π(G), let the degree of p be deg (p)=|{q∈π(G)|q~p}|, and D(G):=( deg (p1), deg (p2),…, deg (pk)). In this paper, we prove that if G is a finite group such that D(G)=D(M) and |G|=|M|, where M is one of the following simple groups: (1) sporadic simple groups, (2) alternating groups Apwith p and p-2 primes, (3) some simple groups of Lie type, then G≅M. Moreover, we show that if G is a finite group with OC (G)={29.39.5.7, 13}, then G≅S6(3) or O7(3), and finally, we show that if G is a finite group such that |G|=29.39.5.7.13 and D(G)=(3,2,2,1,0), then G≅S6(3) or O7(3).

scholarly journals Reduced fusion systems over p-groups with abelian subgroup of index p: III

2019 ◽  
Vol 150 (3) ◽  
pp. 1187-1239
Author(s):  
Bob Oliver ◽  
Albert Ruiz
Keyword(s):  
Abelian Subgroup ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Fusion Systems

AbstractWe finish the classification, begun in two earlier papers, of all simple fusion systems over finite nonabelian p-groups with an abelian subgroup of index p. In particular, this gives many new examples illustrating the enormous variety of exotic examples that can arise. In addition, we classify all simple fusion systems over infinite nonabelian discrete p-toral groups with an abelian subgroup of index p. In all of these cases (finite or infinite), we reduce the problem to one of listing all 𝔽pG-modules (for G finite) satisfying certain conditions: a problem which was solved in the earlier paper [15] using the classification of finite simple groups.

scholarly journals The Coset lattices of E. S. Barnes and G. E. Wall

1990 ◽  
Vol 49 (3) ◽  
pp. 418-433
Author(s):  
Alexander J. Hahn
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Piecewise Linear ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Special Cases ◽  
Sporadic Simple Groups ◽  
Dimension 2 ◽  
Simple Chevalley Group ◽  
Subsequent Literature

AbstractJohn Conway's analysis in 1968 of the automorphism group of the Leech lattice and his discovery of three sporadic simple groups led to the immediate speculation that other Z-lattices might have interesting automorphism groups which give rise to (possibly new) finite simple groups. (The classification theorem for the finite simple groups has since told us that no new finite simple groups can arise in this or any other way.) For example in 1973, M. Broué and M. Enguehard constructed, in every dimension 2n, an even lattice (unimodular if n is odd) whose automorphism group is related to the simple Chevalley group of type Dn. This family of integral lattices received attention and acclaim in the subsequent literature. What escaped the attention of this literature, however, was the fact that these lattices had been discovered years earlier. Indeed in 1959, E. S. Barnes and G. E. Wall gave a uniform construction for a large class of positive definite Z-lattices in dimensions 2n which include those of Broué and Enguehard as special cases. The present article introduces an abstracted and generalized version of the construction of Barnes and Wall. In addition, there are some new observations about Barnes-Wall lattices. In particular, it is shown how to associate to each such lattice a continuous, piecewise linear graph in the plane from which all the important properties of the lattice, for example, its minimum, whether it is integral, unimodular, even, or perfect can be read off directly.

scholarly journals Generators for maximal subgroups of Conway group Co1

2019 ◽  
Vol 17 (1) ◽  
pp. 297-312
Author(s):  
Faisal Yasin ◽  
Adeel Farooq ◽  
Waqas Nazeer ◽  
Shin Min Kang
Keyword(s):  
Maximal Subgroups ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Sporadic Simple Groups

Abstract The Conway groups are the three sporadic simple groups Co1, Co2 and Co3. There are total of 22 maximal subgroups of Co1 and generators of 6 maximal subgroups are provided in web Atlas of finite simple groups. The aim of this paper is to give generators of remaining 16 maximal subgroups.

scholarly journals Involutions in the Automorphism Groups of Small Sporadic Simple Groups

Algebra ◽  
2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Chris Bates ◽  
Peter Rowley ◽  
Paul Taylor
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Sporadic Simple Groups

For each of fifteen of the sporadic finite simple groups we determine the suborbits of its automorphism group in its conjugation action upon its involutions. Representatives are obtained as words in standard generators.

scholarly journals ON A DESIGN FROM PRIMITIVE REPRESENTATIONS OF THE FINITE SIMPLE GROUPS

2019 ◽  
pp. 771
Author(s):  
Ali Reza Rahimipour
Keyword(s):  
Automorphism Group ◽  
Simple Group ◽  
Finite Simple Group ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Full Automorphism Group ◽  
Sporadic Simple Groups ◽  
Design Construction

In this paper we present a design construction from primitive permutation representations of a finite simple group G. The group G acts primitively onthe points and transitively on the blocks of the design. The construction has this property that with some conditions we can obtain t-design for t >=2. We examine our design for fourteen sporadic simple groups. As a result we found a 2-(176,5,4) design with full automorphism group M22.

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