Finite groups with few conjugate classes of minimal non-abelian subgroups

2025/08/13 by Qu, Haipeng, Zhang, Junqiang
#20D15 #20D20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2508.09706

Abstract

Let G be a finite non-abelian group and κ₁(G) the number of conjugate classes of minimal non-abelian subgroups of G. The structure of G with κ₁(G)=1 is determined. In the case of G being the p-groups, the structure of G with κ₁(G)\leqslant p is also determined.

Related

• Finite groups with few subgroups not in the Chermak-Delgado lattice
• Multiplying a conjugacy class by its inverse in a finite group
• A note on finite groups with few conjugacy classes of subgroups
• The conjugacy class number k(G) - a different perspective
• The classification of the finite groups whose abelian subgroups of equal prime power order are conjugate