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14.32 (1999)

Solved

Extending the classical definition of formations, let us define a formation of (not necessarily finite) groups as a nonempty class of groups closed under taking homomorphic images and subdirect products with finitely many factors. Must every first-order axiomatizable formation of groups be a variety?

Contributor: A. M. Gaglione, D. Spellman

Progress

No, every variety of groups that contains a finite nonsolvable member contains an axiomatic subformation that is not a variety (K. A. Kearnes, J. Group Theory, 13, No. 2 (2010), 233–241).

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