Why are the sporadic simple groups HUGE?

Sporadic Groups and Where to Find Them - Theo Johnson-Freyd

My goal is to show you most of the sporadic simple groups in their natural habitats. ... are all large primes and pretty boring. The “small ...

Thompson's sporadic group uniquely determined by the centralizer ...

Wilson, A presentation for the Thompson sporadic simple group, in: W.M. ... Construction of large permutation representations for matrix groups II. Appl ...

Pariah moonshine - OpenScholar

Curiously, the classification features twenty-six exceptional examples—the sporadic simple groups—that do not ... Griess “friendly giant”. Invent. Math. 78 ...

The covering numbers of the sporadic simple groups - SpringerLink

The covering numbers (cn) and the extended covering number (ecn) of all the sporadic simple groups and some other large groups are computed, using “e.

Theory of Groups: a Key To the Mysteries of Math - The New York ...

A special class of finite groups is finite simple groups, and they have attracted all of the recent attention. All groups can be transformed, or ...

Sporadic Group -- from Wolfram MathWorld

The sporadic groups are the 26 finite simple groups that do not fit into any of the four infinite families of finite simple groups (i.e., the cyclic groups ...

A Brief History of the Classification of Finite Simple Groups

(d) one of 26 sporadic finite simple groups: the five Mathieu groups, the four ... large simple groups, while numerous anomalies arise for small ...

What are...sporadic groups? - YouTube

... enormous-theorem-classification-finite-simple-groups Background ... sporadic groups? 934 views · 1 year ago #combinatorics #grouptheory ...

Sporadic group - Wikipedia - X10 host

In the mathematical classification of finite simple groups, there are a number of groups which do not fit into any infinite family.

POLYTOPES DERIVED FROM SPORADIC SIMPLE GROUPS

2000 Mathematics Subject Classification. 51M20, 20F65, 52B15. Key words and phrases. Abstract polytopes, sporadic simple groups, Mathieu group,. Janko group, ...

Base sizes for sporadic simple groups - Department of Mathematics

... large' H-orbits to allow one to decide if b(G) = 2 or 3. We refer ... theory of the almost simple sporadic groups. The Web Atlas [32] ...

An enormous theorem: the classification of finite simple groups

This article does a fine job of disspelling the myth that group theory has no post-classification future. There is no scientific basis for this ...

Semi-Presentations for the Sporadic Simple Groups - EMIS

For example, if G is a small degree permutation group and H is a group of matrices of very large dimension, we can use θ to turn difficult calculations in H ...

Rigid local systems and Sporadic simple groups - Princeton Math

Rigid local systems, Monodromy groups, Sporadic simple groups. The ... large enough ground field Fq/Fp, this twisting factor reduces mod ` to 1 in ...

A Conjecture of Frobenius and the Sporadic Simple Groups, II - jstor

large digit numbers. Then we have only six possibilities for Q: (i) 2 = {1},. (ii) Q = Ord(G),. (iii) Q = {1, 2, 3, 4, 5,10,11) and G is the Mathieu group M12,.

Freshman Seminar University of California, Irvine - UCI Mathematics

It is now known that the finite simple groups consist of the groups that make up the 18 regular families of groups, together with the 26 sporadic groups, and no.

New Upper Bounds on the Spreads of Some Large Sporadic Groups

Few bounds on the spread of finite simple groups are known. In this paper we present improved upper bounds for the spread of many of the ...

Chapter 7: Large Nilpotent Subgroups of Sporadic Simple Groups

Proposition: Let G be a sporadic simple group, let U be a nontrivial nilpotent subgroup in G, and let N_G(U) denote the normalizer of U in G.

View of Local Fusion Graphs and Sporadic Simple Groups

There, examples are given of groups which have local fusion graphs. whose diameter can be arbitrarily large. Local fusion graphs have even being pressed into.

(PDF) 3/2—Generation of the sporadic simple groups - ResearchGate

This conjecture has recently been reduced to the almost simple groups and results of Piccard (1939) and Woldar (1994) show that the conjecture ...