The class $\mathcal{M}\mathcal{N}$ of groups in which all maximal subgroups are normal

We investigate the class $\mathcal{M}\mathcal{N}$ of groups with the property that all maximal subgroups are normal. The class $\mathcal{M}\mathcal{N}$ appeared in the framework of the study of potential counter-examples to the Andrews-Curtis conjecture. In this note we give various structural properties of groups in $\mathcal{M}\mathcal{N}$ and present examples of groups in $\mathcal{M}\mathcal{N}$ and not in $\mathcal{M}\mathcal{N}$.