**Congruence Lattices of Finite Algebras**

by William DeMeo

**Publisher**: arXiv 2012**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.

Download or read it online for free here:

**Download link**

(980KB, PDF)

## Similar books

**Lectures on Topics In The Theory of Infinite Groups**

by

**B.H. Neumann**-

**Tata Institute of Fundamental Research**

As the title suggests, the aim was not a systematic treatment of infinite groups. Instead the author tried to present some of the methods and results that are new and look promising, and that have not yet found their way into the books.

(

**6525**views)

**Group Characters, Symmetric Functions, and the Hecke Algebra**

by

**David M. Goldschmidt**-

**American Mathematical Society**

The book covers a set of interrelated topics, presenting a self-contained exposition of the algebra behind the Jones polynomial along with various excursions into related areas. Directed at graduate students and mathematicians.

(

**8555**views)

**Representation Theory of Compact Groups**

by

**Michael Ruzhansky, Ville Turunen**-

**Aalto TKK**

Contents: Groups (Groups without topology, Group actions and representations); Topological groups (Compact groups, Haar measure, Fourier transforms on compact groups..); Linear Lie groups (Exponential map, Lie groups and Lie algebras); Hopf algebras.

(

**7691**views)

**Lectures on Algebraic Groups**

by

**Alexander Kleshchev**-

**University of Oregon**

Contents: General Algebra; Commutative Algebra; Affine and Projective Algebraic Sets; Varieties; Morphisms; Tangent spaces; Complete Varieties; Basic Concepts; Lie algebra of an algebraic group; Quotients; Semisimple and unipotent elements; etc.

(

**8521**views)