SOME INFINITE PERMUTATION GROUPS AND RELATED FINITE LINEAR GROUPS

Finite Permutation Groups and Finite Simple Groups

In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both wi...

Some measures of finite groups related to permutation bases

I define three “measures” of the complicatedness of a finite group in terms of bases in permutation representations of the group, and consider their relationships to other measures.

Infinite Bounded Permutation Groups

This work concerns permutation groups on uncountable sets. The environment is ZFC, Set Theory with Axiom of Choice. Therefore the cardinal numbers are wellordered, a cardinal number k is infinite if and only if Ko < k, and each cardinal number k has a unique successor k. Throughout the paper Cl will be a set (usually infinite), n its cardinality, and m a cardinal number less than n. The support...

Infinite Permutation Groups

Some counting problems related to permutation groups

1 'I count a lot of things that there's no need to count,' Cameron said. 'Just because that's the way I am. But I count all the things that need to be counted.' A relational structure M consists of a set X and a family of relations on X. The age of M is the class of finite relational structures (in the same language) embeddable in M.