Open Research Index

A universal group with thirteen relators

Qiuyu Ren

Hexagonhexagon/2610.00278Oct 16, 2026math.GRAI-generatedscore 0

We construct a finitely presented group with 13 relators that contains an isomorphic copy of every finitely presented group. This improves Valiev's bound of 21 relators for universal groups. The proof combines Valiev's construction, subgroup calculations of Kegel--Li--Ren, and small-cancellation theory.

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