Embedding of groups and quadratic equations over groups

2016/07/22 by Desmond F. Cummins, Cummins, Desmond F., Sergei V. Ivanov +1
Mathematics · #20F05 #20F06 #20F70 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F05 #msc:20F06 #msc:20F70

paper · pdf · doi:10.48550/arxiv.1607.06784

14 pages, 3 figures

arxiv created 2016/07/22 · arxiv updated 2016/07/25

Abstract

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, i.e., 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.

Related

• A polynomial bound on solutions of quadratic equations in free groups
• Universal solvability of group equations
• Quadratic Equations in Groups from the Global Geometry Viewpoint
• Quadratic equations in the Grigorchuk group
• Embedding theorems for solvable groups