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The Moebius function on the lattice of normal subgroups

Gregory M Constantine

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.

The Moebius function on the lattice of normal subgroups

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.

Paper Structure

This paper contains 4 sections, 31 equations.

Table of Contents

  1. 1. The lattice of normal subgroups
  2. 2. Conjugacy classes that generate a group
  3. 3. Class restrictions on the major subgroups
  4. 4. Faithful irreducible representations