Let \(G=K\ltimes A\) be the semidirect product group of a compact group K acting on an abelian locally compact group A. In (Vershik and Karpushev Mathematics of the USSR-Sbornik 47:513–526, 1984), Vershik and Karpushev defined the cortex of G, cor(G), as the set of all \(\pi \in {\widehat{G}}\) that cannot be Hausdorff separated from the identity representation \(1_G\) of G. Using Baggett’s topology, we describe the cortex of G in terms of the trivial representation \(1_H\) of some (unique) subgroup H of K. As an application, we have treated some examples of semidirect products.
