Representations of Posets and Indecomposable Torsion-Free Abelian Groups

The Class of (2, 2)-Groups With Homocyclic Regulator Quotient of Exponent Has Bounded representation type

“…If the p-local, p-reduced almost completely decomposable group G = H ⊕ L is decomposable, then H, L may be assumed to be given by coordinate matrices δ H , δ L . Since the critical typeset of G is an inverted forest, we have R(G) = R(H) ⊕ R(L); see [5,Lemma 3.1]. Thus G has the coordinate matrix δ G = δ H ⊕ δ L .…”

“…and a summand of type 2, 4, A D , 1 p ; see (5) in the list of rank 4. Hence, omitting all those summands, there is no 0-row in D .…”

Completely decomposable direct summands of torsion-free abelian groups of finite rank

“…Then T cr (X) is called the critical typeset of X. The problem has been largely solved when the critical typeset is an inverted forest in a number of papers by Arnold-Mader-Mutzbauer-Solak ( [2], [3], [4], [5], [6], [7], [8], [9], [10]) using representations of posets as a tool.…”