Algebraic commutators with respect to subnormal subgroups in division\n rings

2020/11/03 by Mai Hoang Bien, Bien, Mai Hoang, Bui Xuan Hai +3
Mathematics · #Advanced Topics in Algebra #Finite Group Theory Research #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2011.01911

Abstract

Let D be a division ring and K a subfield of D which is not necessarily\ncontained in the center F of D. In this paper, we study the structure of\nD under the condition of left algebraicity of certain subsets of D over\nK. Among results, it is proved that if D^* contains a noncentral normal\nsubgroup which is left algebraic over K of bounded degree d, then [D:F]\≤\nd². In case K=F, the obtained results show that if either all additive\ncommutators or all multiplicative commutators with respect to a noncentral\nsubnormal subgroup of D^* are algebraic of bounded degree d over F, then\n[D:F]\≤ d².\n

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