Abstract
We study equations of the form ( α = x), which are single axioms for groups of exponent 4, where α is a term in product only. Every such α must have at least nine variable occurrences, and there are exactly three such α of this size, up to variable renaming and mirroring. These terms were found by an exhaustive search through all terms of this form. Automated techniques were used in two ways: to eliminate many α by verifying that ( α = x) is ture in some nongroup, and to verify that the group axioms do indeed follow from the successful ( α = x). We also present an improvement on Neumann's scheme for single axioms for varieties of groups.
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