A group G is called metamodular if for each subgroup H of G either the subgroup lattice 𝔏(H) is modular or H is a modular element of the lattice 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-7,
author = {M. De Falco and F. de Giovanni and C. Musella and R. Schmidt},
title = {Groups with metamodular subgroup lattice},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {231-240},
zbl = {1028.20023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-7}
}
M. De Falco; F. de Giovanni; C. Musella; R. Schmidt. Groups with metamodular subgroup lattice. Colloquium Mathematicae, Tome 96 (2003) pp. 231-240. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-7/