Uniqueness of the smallest chameleon in the class of monoids

Nicholas Johnston; Edmond W.H. Lee; Vehbi E. Paksoy

doi:10.1016/j.exco.2025.100209

Uniqueness of the smallest chameleon in the class of monoids

Nicholas Johnston
, Edmond W.H. Lee
, Vehbi E. Paksoy

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A semigroup is a chameleon if it is the reduct of both a finitely based involution semigroup and a non-finitely based involution semigroup. Recently, a certain monoid K of order six was shown to be a smallest chameleon in the class of monoids. The main objective of the present article is to show that although there exist 2237 monoids of order six up to isomorphism, examples of chameleons different from K do not exist. Consequently, up to isomorphism, K is the unique smallest example of chameleon in the class of monoids.

Original language	English
Article number	100209
Number of pages	3
Journal	Examples and Counterexamples
Volume	8
DOIs	https://doi.org/10.1016/j.exco.2025.100209
State	Published - Dec 2025

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title = "Uniqueness of the smallest chameleon in the class of monoids",

abstract = "A semigroup is a chameleon if it is the reduct of both a finitely based involution semigroup and a non-finitely based involution semigroup. Recently, a certain monoid K of order six was shown to be a smallest chameleon in the class of monoids. The main objective of the present article is to show that although there exist 2237 monoids of order six up to isomorphism, examples of chameleons different from K do not exist. Consequently, up to isomorphism, K is the unique smallest example of chameleon in the class of monoids.",

author = "Nicholas Johnston and Lee, \{Edmond W.H.\} and Paksoy, \{Vehbi E.\}",

year = "2025",

month = dec,

doi = "10.1016/j.exco.2025.100209",

language = "English",

volume = "8",

journal = "Examples and Counterexamples",

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T1 - Uniqueness of the smallest chameleon in the class of monoids

AU - Johnston, Nicholas

AU - Lee, Edmond W.H.

AU - Paksoy, Vehbi E.

PY - 2025/12

Y1 - 2025/12

N2 - A semigroup is a chameleon if it is the reduct of both a finitely based involution semigroup and a non-finitely based involution semigroup. Recently, a certain monoid K of order six was shown to be a smallest chameleon in the class of monoids. The main objective of the present article is to show that although there exist 2237 monoids of order six up to isomorphism, examples of chameleons different from K do not exist. Consequently, up to isomorphism, K is the unique smallest example of chameleon in the class of monoids.

AB - A semigroup is a chameleon if it is the reduct of both a finitely based involution semigroup and a non-finitely based involution semigroup. Recently, a certain monoid K of order six was shown to be a smallest chameleon in the class of monoids. The main objective of the present article is to show that although there exist 2237 monoids of order six up to isomorphism, examples of chameleons different from K do not exist. Consequently, up to isomorphism, K is the unique smallest example of chameleon in the class of monoids.

UR - https://doi.org/10.1016/j.exco.2025.100209

U2 - 10.1016/j.exco.2025.100209

DO - 10.1016/j.exco.2025.100209

M3 - Article

VL - 8

JO - Examples and Counterexamples

JF - Examples and Counterexamples

M1 - 100209

ER -

Uniqueness of the smallest chameleon in the class of monoids

Abstract

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