Free unitary and symmetric pairs in normal subgroups of division rings with involution

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发表日期：

2025年7月30日

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Jairo Z. Gonçalves

摘要

Let D be a division ring with center Z of char ≠ 2, with an involution*. Let D^† be the multiplicative group of D, and let N ⊲ D^† be a normal subgroup. An element u ∈ D^† is said to be symmetric (unitary) if u* = u (respectively u* = u⁻¹). Let $\frak{U}$ $U$ be the group of unitary units of D, and let $N \triangleleft \frak{U}$ $N ◃ U$ be a non-central subgroup. Under some mild conditions we show that N contains a free unitary pair. We also present some results for the presence of free symmetric pairs in N ⊲ D^†.