Small monoids generating varieties with uncountably many subvarieties

Abstract

An algebra that generates a variety with uncountably many subvarieties is said to be of type $2^{\aleph_0}$. We show that the Rees quotient monoid $M(aabb)$ of order ten is of type $2^{\aleph_0}$, thereby affirmatively answering a recent question of Glasson. As a corollary, we exhibit a new example of type $2^{\aleph_0}$ monoid of order six, which turns out to be minimal and the first of its kind that is finitely based.

Theorems & Definitions (9)

• Theorem 1
• Corollary 1
• proof
• Lemma 1: Gusev-Vernikov-18
• Lemma 2
• proof
• Lemma 3
• proof
• proof : Proof of Theorem \ref{['T: M(aabb)']}