2000/09/01 by Victor Bovdi, Bovdi, Victor
Chemistry · Mathematics · #16S34 #20C05 #20C07 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA) #Synthesis and Reactivity of Sulfur-Containing Compounds #Synthesis of heterocyclic compounds #math.GR #math.RA #msc:16S34 #msc:20C05 #msc:20C07
paper · pdf · doi:10.48550/arxiv.math/0009006
11 pages, AMS-TeX, to appear in Comm. in Algebra
arxiv created 2000/09/01 · openalex publication_date 2000/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let U(KG) be the group of units of the group ring KG of the group G over a commutative ring K. The anti-automorphism g↦ g\m1 of G can be extended linearly to an anti-automorphism a↦ a^* of KG. Let S_*(KG)=\x∈ U(KG) | x^*=x\ be the set of all symmetric units of U(KG). We consider the following question: for which groups G and commutative rings K it is true that S_*(KG) is a subgroup in U(KG). We answer this question when either a) G is torsion and K is a commutative G-favourable integral domain of characteristic p≥ 0 or b) G is non-torsion nilpotent group and KG is semiprime.