The solvability of groups with nilpotent minimal coverings

2014/09/26 by Russell D. Blyth, Blyth, Russell D., Francesco Fumagalli +3
Mathematics · #20D15 #20D99 #20E32 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20D15 #msc:20D99 #msc:20E32

paper · pdf · doi:10.48550/arxiv.1409.7501

arxiv created 2014/09/26 · arxiv updated 2014/09/29

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.

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