Embedding of groups and quadratic equations over groups

D. F. Cummins, S. V. Ivanov

Research output: Contribution to journalArticlepeer-review


We prove that, for every integer n ≥ 2, a finite or infinite countable group G can be embedded into a 2-generated group H in such a way that the solvability of quadratic equations of length at most n is preserved, that is, every quadratic equation over G of length at most n has a solution in G if and only if this equation, considered as an equation over H, has a solution in H.

Original languageEnglish (US)
Pages (from-to)99-115
Number of pages17
JournalIllinois Journal of Mathematics
Issue number1
StatePublished - 2016

ASJC Scopus subject areas

  • General Mathematics


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