Representability of permutation representations on coalgebras and the isomorphism problem

Cristina Costoya, David Méndez, Antonio Viruel

Let $G$ be a group and let $\rho :G\to \mathrm{Sym}(V)$ be a permutation representation of $G$ on a set $V$. We prove that there is a faithful $G$-coalgebra $C$ such that $G…