Finite groups whose subgroup graph contains a vertex of large degree

Abstract

Burness and Scott (J Aust Math Soc 87:329-357, 2009) classified finite groups G such that the number of prime order subgroups of G is greater than \(|G|/2-1\). In this note, we study finite groups G whose subgroup graph contains a vertex of degree greater than \(|G|/2-1\). The classification given for finite solvable groups extends the work of Burness and Scott.