The Moebius function on the lattice of normal subgroups

2025/01/30 by Constantine, Gregory M
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2501.18079

Abstract

By studying lattices of normal subgroups, especially those of the socle and radical, an expression is obtained for the minimal number of conjugacy classes required to generate a group. This number is shown to be captured by the character table. The Moebius function is then used to extract information on the faithful irreducible representations of a group.

Related

• The Möbius Function of the Suzuki Groups
• On G-character tables for normal subgroups
• Groups isomorphic to all their non-trivial normal subgroups
• The class MN of groups in which all maximal subgroups are normal
• Socle of Hamiltonian Group