Details

Autor(en) / Beteiligte

• Kearnes, K. A.
• Kiss, E. W.
• Szendrei, Á.
• Willard, R. D.

Titel

Chief Factor Sizes in Finitely Generated Varieties

Ist Teil von

• Canadian journal of mathematics, 2002-08, Vol.54 (4), p.736-756

Ort / Verlag

Cambridge, UK: Cambridge University Press

Erscheinungsjahr

2002

Quelle

Electronic Journals Library

Beschreibungen/Notizen

• Let $\mathbf{A}$ be a $k$ -element algebra whose chief factor size is $c$ . We show that if $\mathbf{B}$ is in the variety generated by $\mathbf{A}$ , then any abelian chief factor of $\mathbf{B}$ that is not strongly abelian has size at most ${{c}^{k-1}}$ . This solves Problem 5 of The Structure of Finite Algebras, by D. Hobby and R. McKenzie. We refine this bound to $c$ in the situation where the variety generated by $\mathbf{A}$ omits type 1. As a generalization, we bound the size of multitraces of types 1, 2, and 3 by extending coordinatization theory. Finally, we exhibit some examples of bad behavior, even in varieties satisfying a congruence identity.