2018/01/01 by Osnel Broche, Del rio, Angel, Jairo Z. Gonçalves +2 · 3 citations
Mathematics · #Finite Group Theory Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · doi:10.1007/s00013-018-1223-8
Let KG be the group algebra of a torsion group G over a field K. We show that if the units of KG satisfy a Laurent polynomial identity, which is not satisfied by the units of the relative free algebra K[α ,β : α 2=β 2=0] K [ α , β : α 2 = β 2 = 0 ] , then KG satisfies a polynomial identity. This extends Hartley’s Conjecture which states that if the units of KG satisfy a group identity, then KG satisfies a polynomial identity. As an application we prove that if the units of KG satisfy a Laurent polynomial identity whose support has cardinality at most 3, then KG satisfies a polynomial identity.