You are here: Seminars > 2025 > April 9th
University of Warwick
Time: 16:00-17:00 (GMT+8), Wednesday April 9th, 2025
Location: Zoom
Abstract:
Let \(G\) be a finite group with a subgroup \(H\). If \(H\) is subnormal, then \(|HK|\) is a divisor of \(|G|\) for any other subgroup \(K\). We observe that the Kegel-Wielandt-Kleidman theorem implies that the converse is also true, namely \(|HK|\) divides \(|G|\) for all \(K\) if and only if \(H\) is subnormal. Some interesting phenomena are related. For example, \(x^{|G:K|} \in K\) for all subgroups \(K\) if and only if \(x\) lies in the Fitting subgroup.
Host: 陈俊彦 Junyan Chen