On subnormal subgroups in division rings containing a non-abelian solvable subgroup

2018/08/28 by Hai, Bui Xuan, Bien, Mai Hoang
#FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1808.09252

Abstract

Let D be a division ring with center F and N a subnormal subgroup of the multiplicative group D^* of D. Assume that N contains a non-abelian solvable subgroup. In this paper, we study the problem on the existence of non-abelian free subgroups in N. In particular, we show that if either N is algebraic over F or F is uncountable, then N contains a non-abelian free subgroup.

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