Logo

Congruence Lattices of Finite Algebras

Small book cover: Congruence Lattices of Finite Algebras

Congruence Lattices of Finite Algebras
by

Publisher: arXiv
Number of pages: 130

Description:
In this work, we review a number of methods for finding a finite algebra with a given congruence lattice, including searching for intervals in subgroup lattices. We also consider methods for proving that algebras with a given congruence lattice exist without actually constructing them. By combining these well known methods with a new method we have developed, we prove that with one possible exception every lattice with at most seven elements is isomorphic to the congruence lattice of a finite algebra.

Home page url

Download or read it online for free here:
Download link
(980KB, PDF)

Similar books

Book cover: Why are Braids Orderable?Why are Braids Orderable?
by
This book is an account of several quite different approaches to Artin's braid groups, involving self-distributive algebra, uniform finite trees, combinatorial group theory, mapping class groups, laminations, and hyperbolic geometry.
(7830 views)
Book cover: Elements of Group TheoryElements of Group Theory
by - arXiv
The following notes are the basis for a graduate course. They are oriented towards the application of group theory to particle physics, although some of it can be used for general quantum mechanics. They have no pretense of mathematical rigor.
(10953 views)
Book cover: Groups as GraphsGroups as Graphs
by - CuArt
In this book, for the first time, the authors represented every finite group in the form of a graph. This study is significant because properties of groups can be immediately obtained by looking at the graphs of the groups.
(7423 views)
Book cover: An Introduction to Group Theory: Applications to Mathematical Music TheoryAn Introduction to Group Theory: Applications to Mathematical Music Theory
by - BookBoon
In this text, a modern presentation of the fundamental notions of Group Theory is chosen, where the language of commutative diagrams and universal properties, so necessary in Modern Mathematics, in Physics and Computer Science, is introduced.
(6129 views)