The Moebius function on the lattice of normal subgroups
Group Theory
2025-01-31 v1 Combinatorics
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.
Cite
@article{arxiv.2501.18079,
title = {The Moebius function on the lattice of normal subgroups},
author = {Gregory M Constantine},
journal= {arXiv preprint arXiv:2501.18079},
year = {2025}
}