Atoms of the relative block monoid
Nicholas R. Baeth, Justin Hoffmeier · Involve a Journal of Mathematics · 2009
Let G be a finite abelian group with subgroup H and let Ᏺ(G) denote the free abelian monoid with basis G.The classical block monoid Ꮾ(G) is the collection of sequences in Ᏺ(G) whose elements sum to zero.The relative block monoid Ꮾ H (G), defined by Halter-Koch, is the collection of all sequences in Ᏺ(G) whose elements sum to an element in H .We use a natural transfer homomorphism θ : Ꮾ H (G) → Ꮾ(G/H ) to enumerate the irreducible elements of Ꮾ H (G) given an enumeration of the irreducible elements of Ꮾ(G/H ).