On subnormal subgroups of skew fields
Let D be a skew field with center Z, F be a free group with two generators \(x_ 1\), \(x_ 2\), \(D\{x_ 1,x_ 2\}=D*_ ZZF\) be the free product over Z, where ZF is the group ring. The author calls \(P(x_ 1,x_ 2)\in D\{x_ 1,x_ 2\}\setminus D\) a generalized Laurent polynomial. It is proved that if Z is infinite and \([D:Z]=\infty\) then any subnormal subgroup of \(D^*\) which satisfies a Laurent generalized polynomial identity is central.
scientific article; zbMATH DE number 4051827