The solvability of groups with nilpotent minimal coverings
Group Theory
2014-09-29 v1
Abstract
A covering of a group is a finite set of proper subgroups whose union is the whole group. A covering is minimal if there is no covering of smaller cardinality, and it is nilpotent if all its members are nilpotent subgroups. We complete a proof that every group that has a nilpotent minimal covering is solvable, starting from the previously known result that a minimal counterexample is an almost simple finite group.
Keywords
Cite
@article{arxiv.1409.7501,
title = {The solvability of groups with nilpotent minimal coverings},
author = {Russell D. Blyth and Francesco Fumagalli and Marta Morigi},
journal= {arXiv preprint arXiv:1409.7501},
year = {2014}
}