|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Finite basis problem
for involution semigroups of order four
Meng Gao, Edmond W. H. Lee, Yan Feng Luo and Wen Ting Zhang |
|
Vol. 342 (2026), No. 1, 163–206
|
 |
Abstract |
|
Since the 1980s, it has been known that the smallest non-finitely based semigroups are of order six. Surprisingly, for involution semigroups, a non-finitely based example of order five was recently discovered. In this article, it is confirmed that every involution semigroup of order four is finitely based. Since every involution semigroup of order three or less is already known to be finitely based, it follows that the smallest non-finitely based involution semigroups are of order five. |
Keywords
semigroup, involution semigroup, identity basis, finitely
based, finite basis problem
|
Mathematical Subject Classification
Primary: 20M05
|
Milestones
Received: 11 March 2025
Revised: 13 January 2026
Accepted: 14 January 2026
Published: 23 March 2026
|
Authors |
| Meng Gao | |
| School of Mathematics and
Statistics Lanzhou University Lanzhou, Gansu China |
|
| Edmond W. H. Lee | |
| Department of Mathematics Nova Southeastern University Fort Lauderdale, FL United States |
|
| Yan Feng Luo | |
| School of Mathematics and
Statistics Lanzhou University Lanzhou, Gansu China |
|
| Wen Ting Zhang | |
| School of Mathematics and
Statistics Lanzhou University Lanzhou, Gansu China |
|
| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
