On Finitely Based Groups and Nonfinitely Based Quasivarieties

✍ Scribed by John Lawrence; Ross Willard

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 171 KB
• Volume: 203
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1997.7470

✦ Synopsis

We define the notion of strictly finitely based varieties of groups and determine which finite groups are strictly finitely based. Then we use this result to prove the existence of "very nonfinitely based" finite algebras, thereby solving two open problems in the theory of quasivarieties.