Burnside kei

Burnside Orders, Burnside Algebras and Partition Lattices

The permutation representation theory of groups has been extended, through quasigroups, to one-sided left (or right) quasigroups. The current paper establishes a link with the theory of ordered sets, introducing the concept of a Burnside order that generalizes the poset of conjugacy classes of subgroups of a finite group. Use of the Burnside order leads to a simplification in the proof of key p...

2 Kei - Chun

Tools for performance monitoring and analysis become indispensable parts of programming environments for parallel computers. As the number of processors increases, the conventional techniques for monitoring the performance of parallel programs will produce large amounts of data in the form of event trace les. On the other hand, this wealth of information is a problem for the programmer who is f...

Burnside rings

1 Let G be a finite group. The Burnside ring B(G) of the group G is one of the fundamental representation rings of G, namely the ring of permutation representations. It is in many ways the universal object to consider when looking at the category of G-sets. It can be viewed as an analogue of the ring Z of integers for this category. It can be studied from different points of view. First B(G) is...

Reading Burnside

In this note, we simply (try to) interpret Burnside’s original proof in modern terminology and notation. This is instructive for anyone interested in the evolution of mathematical writing, as Burnside’s language is – at least for the author – essentially unreadable as a rigorous mathematical proof. One can make sense of it, with some effort, and from it construct a proof which is (or at least, ...

Free Burnside Semigroups