Groups with 5 nontrivial conjugacy classes of non self-normalizing subgroups are solvable

2025/02/20 by Loukaki, Maria
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2502.14480

Abstract

For any n nonnegative integer a family of groups, denoted by D_n , was introduce by Bianchi et al., as the collection of all finite groups with exactly n conjugacy classes of nontrivial, non self-normalizing subgroups. It was conjectured that D₅ consists of solvable groups with derived length at most 3. In this note we verify their conjecture.

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