A note on "A minimal congruence lattice representation for $\mathbb M_{p+1}$''

TL;DR

This paper revisits a theorem about the minimal size of congruence lattice representations for a specific algebraic structure, confirming it has size 2p and relates to a regular D_{2p}-set.

Contribution

It provides a reproof of a known theorem, clarifying the structure and size of minimal congruence lattice representations for  M_{p+1}.

Findings

Minimal congruence lattice representation size is 2p.

Such representations are expansions of regular D_{2p}-sets.

The proof offers new insights into the structure of these representations.

Abstract

We reprove a theorem of Bunn, Grow, Insall, and Thiem, which asserts that a minimal congruence lattice representation for $\mathbb M_{p+1}$ has size $2p$, and is an expansion of a regular $D_{2p}$-set.