Results 1 
9 of
9
SATURATED FUSION SYSTEMS OVER 2GROUPS
"... Abstract. We develop methods for listing, for a given 2group S, all nonconstrained centerfree saturated fusion systems over S. These are the saturated fusion systems which could, potentially, include minimal examples of exotic fusion systems: fusion systems not arising from any finite group. To tes ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
Abstract. We develop methods for listing, for a given 2group S, all nonconstrained centerfree saturated fusion systems over S. These are the saturated fusion systems which could, potentially, include minimal examples of exotic fusion systems: fusion systems not arising from any finite group. To test our methods, we carry out this program over four concrete examples: two of order 2 7 and two of order 2 10. Our long term goal is to make a wider, more systematic search for exotic fusion systems over 2groups of small order. For any prime p and any finite pgroup S, a saturated fusion system over S is a category F whose objects are the subgroups of S, whose morphisms are injective group homomorphisms between the objects, and which satisfy certain axioms due to Puig and described here in Section 2. Among the motivating examples are the categories F = FS(G) where G is a finite group with Sylow psubgroup S: the morphisms in FS(G) are the group homomorphisms between subgroups of S which are induced by conjugation by elements of G. A saturated fusion system F which does not arise in this fashion from a group is called “exotic”.
Simultaneous Constructions of the Sporadic Groups Co2
, 906
"... Abstract. In this article we give selfcontained existence proofs for the sporadic simple groups Co2 and Fi22 using the second author’s algorithm [10] constructing finite simple groups from irreducible subgroups of GLn(2). These two sporadic groups were originally discovered by J. Conway [4] and B. ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Abstract. In this article we give selfcontained existence proofs for the sporadic simple groups Co2 and Fi22 using the second author’s algorithm [10] constructing finite simple groups from irreducible subgroups of GLn(2). These two sporadic groups were originally discovered by J. Conway [4] and B. Fischer [7], respectively, by means of completely different and unrelated methods. In this article n = 10 and the irreducible subgroups are the Mathieu group M22 and its automorphism group Aut(M22). We construct their five nonisomorphic extensions Ei by the two 10dimensional nonisomorphic simple modules of M22 and by the two 10dimensional simple modules of A22 = Aut(M22) over F = GF(2). In two cases we construct the centralizer Hi = CG i (zi) of a 2central involution zi of Ei in any target simple group Gi. Then we prove that all the conditions of Algorithm 7.4.8 of [11] are satisfied. This allows us to construct G3 ∼ = Co2 inside GL23(13) and G2 ∼ = Fi22 inside GL78(13). We also calculate their character tables and presentations. 1.
Coding theory and algebraic combinatorics
, 2008
"... This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings, kissing numbers, lattices, and association schemes. In part ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings, kissing numbers, lattices, and association schemes. In particular, special interest is devoted to the relationship between codes and combinatorial designs. We describe and recapitulate important results in the development of the state of the art. In addition, we give illustrative examples and constructions, and highlight recent advances. Finally, we provide a collection of significant open problems and challenges concerning future research.
STRONGLY CLOSED SUBGROUPS OF FINITE GROUPS
, 809
"... Abstract. This paper gives a complete classification of the finite groups that contain a strongly closed psubgroup for p any prime. 1. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. This paper gives a complete classification of the finite groups that contain a strongly closed psubgroup for p any prime. 1.
The Classification of the Finite Simple Groups: An Overview
 MONOGRAFÍAS DE LA REAL ACADEMIA DE CIENCIAS DE ZARAGOZA. 26: 89–104, (2004)
, 2004
"... ..."
computed. It follows that G and Fi23 have the same character table. REPRESENTATION THEORETIC EXISTENCE PROOF FOR FISCHER GROUP Fi23 3
, 2008
"... In the first section of this senior thesis the author provides some new efficient algorithms for calculating with finite permutation groups. They cannot be found in the computer algebra system Magma, but they can be implemented there. For any finite group G with a given set of generators, the algori ..."
Abstract
 Add to MetaCart
In the first section of this senior thesis the author provides some new efficient algorithms for calculating with finite permutation groups. They cannot be found in the computer algebra system Magma, but they can be implemented there. For any finite group G with a given set of generators, the algorithms calculate generators of a fixed subgroup of G as short words in terms of original generators. Another new algorithm provides such a short word for a given element of G. These algorithms are very useful for documentation and performing demanding experiments in computational group theory. In the later sections, the author gives a selfcontained existence proof for Fischer’s sporadic simple group Fi23 of order 2 18 · 3 13 · 5 2 · 7 · 11 · 13 · 17 · 23 using G. Michler’s Algorithm [11] constructing finite simple groups from irreducible subgroups of GLn(2). This sporadic group was originally discovered by B. Fischer in [6] by investigating 3transposition groups, see also [5]. This thesis gives a representation theoretic and algorithmic existence proof for his group. The author constructs