Subnormal subgroups in division rings with generalized power central group identities

摘要

Let be a division ring with center . The aim of the paper is to show that if is uncountable or is finite dimensional over , then every subnormal subgroup of the multiplicative group of satisfying a nontrivial generalized power central group identity is contained in . As a corollary, Conjecture 2 in (Herstein, Israel J Math 31:180-188, 1978) holds in case is finite dimensional.