On quasivarieties of groups and equations over groups

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A proof is given that the quasivariety of groups generated by finite and torsion-free groups does not contain the class of periodic groups. This result is related to (and inspired by) the solvability of equations over groups. The proof uses the Feit-Thompson theorem on the solvability of finite groups of odd order as well as Kostrikin-Zelmanov results on the restricted Burnside problem, and applies technical details of a recent construction of weakly finitely presented periodic groups.

Original languageEnglish (US)
Pages (from-to)67-74
Number of pages8
JournalBulletin of the London Mathematical Society
Issue number1
StatePublished - 2005

ASJC Scopus subject areas

  • General Mathematics


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