Groups with metamodular subgroup lattice
Volume 95 / 2003
Colloquium Mathematicum 95 (2003), 231-240
MSC: Primary 20F24.
DOI: 10.4064/cm95-2-7
Abstract
A group $G$ is called metamodular if for each subgroup $H$ of $G$ either the subgroup lattice ${{{\mathfrak L}}}(H)$ is modular or $H$ is a modular element of the lattice ${{{\mathfrak L}}}(G)$. Metamodular groups appear as the natural lattice analogues of groups in which every non-abelian subgroup is normal; these latter groups have been studied by Romalis and Sesekin, and here their results are extended to metamodular groups.
