Chief factor sizes in finitely generated varieties
by
Emil W. Kiss
Eötvös University, Budapest

A chief factor of a finite algebra A is a congruence \beta/\alpha of the factor algebra A/\alpha, where \beta covers \alpha in the congruence lattice of A. The size of this chief factor is the maximal size of its congruence blocks. In this lecture we present results of Keith Kearnes, Emil W. Kiss, and Ágnes Szendrei concerning the following question. Given an n-element algebra A whose maximal chief factor size is b, what can be said about the sizes of the chief factors of the finite algebras in the variety generated by A? A problem of Ralph McKenzie is solved by showing that b⁽n-1) bounds the size of every chief factor that is Abelian, but not strongly Abelian. If the variety generated by A omits type 1 of tame congruence theory, then in fact each Abelian chief factor has size at most b. Examples of bad behavior are also exhibited, even in varieties satisfying a congruence identity.

Date received: July 30, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadj-20.