English

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}
}