| In this thesis we explore atoms, or minimal zero-sum sequences, in block monoids over finite abelian groups. Two algorithms are described for enumerating these atoms. The total number of atoms are given for the block monoids over all finite abelian groups of order up to 101. Conjectures are then made that compare the number of atoms of certain lengths in block monoids over groups with the same order. Evidence, both computational and theoretical, is given to support these conjectures. |
