It is shown that if in the factorization of a finite cyclic group each factor has either prime power order or order equal to the product of two primes then one factor must be periodic. This is shown to be the best possible result of this type.  2004 Elsevier Inc. All rights reserved.

The Algebraicity Conjecture treats model-theoretic foundations of algebraic group theory. It states that any simple group of finite Morley rank is an algebraic group over an algebraically closed field. In the mid-1990s a view was consolidated that this project falls into four cases of different flavour: even type, mixed type, odd type, and degenerate type. This book contains a proof of the conj...

There are two major types of ultrafilters, principal ultrafilters and non-principal ultrafilters. A principal ultrafilter is one that is generated by any single element a ∈ S, and has the form 〈a〉 = {A ⊆ S | a ∈ A}. However, these principal ultrafilters are not incredibly interesting, and will be used only as an example in this document. On the other hand, we have non-principal ultrafilters. We...

Representations of finite groups are much simpler than those of larger ones, but they offer a model for the general theory and for that reason are very valuable as an introduction to the subject. The challenge is to present the material in such a way as to give some idea of techniques that might generalize, rather than use tricks that definitely work only for finite groups. Pursuing this goal s...

This paper classifies the maximal finite subgroups of Sp 2n (Q) for 1 ≤ n ≤ 11 up to conjugacy in GL2n(Q).