Are there free groups in division rings?
The authors approach the following conjecture 1. Any noncentral subnormal subgroup of the multiplicative group \(D^*\) of a skew field D contains a free subgroup of rank two. They show that this conjecture holds in some special cases when the original skew field contains an appropriate finite dimensional skew field. They also investigate the following weaker conjecture 2. A word from a free group defines a substitution mapping of \(D^*\) to \(D^*\). The conjecture is that any such mapping cannot map a noncentral subnormal subgroup of \(D^*\) into the center of D. The authors provide several examples of words for which this conjecture is true.
scientific article; zbMATH DE number 3961879