On the transitivity of Gassmann triples. (Q2855681)

Let \(G\) be a finite group. Two subgroups \(H_1\) and \(H_2\) of \(G\) are Gassmann equivalent if \(|c^G\cap H_1|=|c^G\cap H_2|\) for all \(c\in G\), where \(c^G\) is the conjugacy class of \(c\) in \(G\), and \((G,H_1,H_2)\) is called a Gassmann triple.NEWLINENEWLINE It is known that \(|H_1|=|H_2|\) in Gassmann triples. The paper under review discusses some examples and considers questions such as if \((G,H,K)\) and \((G,H,L)\) are Gassmann triples, when is \((G,K,L)\) a Gassmann triple? Behavior of Gassmann triples under direct products and quotient groups is also studied.