@phdthesis{Solak2007,
  author    = {Solak, Ebru},
  title     = {Almost Completely Decomposable Groups of Type (1,2)},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-24794},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2007},
  abstract  = {A torsion free abelian group of finite rank is called almost completely decomposable if it has a completely decomposable subgroup of finite index. A p-local, p-reduced almost completely decomposable group of type (1,2) is briefly called a (1,2)-group. Almost completely decomposable groups can be represented by matrices over the ring Z/hZ, where h is the exponent of the regulator quotient. This particular choice of representation allows for a better investigation of the decomposability of the group. Arnold and Dugas showed in several of their works that (1,2)-groups with regulator quotient of exponent at least p^7 allow infinitely many isomorphism types of indecomposable groups. It is not known if the exponent 7 is minimal. In this dissertation, this problem is addressed.},
  language  = {en}
}
@phdthesis{Nahler2001,
  author    = {Nahler, Michael},
  title     = {Isomorphism classes of almost completely decomposable groups},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-2817},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2001},
  abstract  = {In this thesis we investigate near-isomorphism classes and isomorphism classes of almost completely decomposable groups. In Chapter 2 we introduce the concept of almost completely decomposable groups and sum up their most important facts. A local group is an almost completely decomposable group with a primary regulator quotient. A uniform group is a rigid local group with a homocyclic regulator quotient. In Chapter 3 a weakening of isomorphism, called type-isomorphism, appears. It is shown that type-isomorphism agrees with Lady's near-isomorphism. By the Main Decomposition Theorem and the Primary Reduction Theorem we are allowed to restrict ourselves on clipped local groups, namely groups without a direct rank-one summand. In Chapter 4 we collect facts of matrices over commutative rings with an identity element. Matrices over the local ring (Z / p^e Z) of residue classes of the rational integers modulo a prime power play an important role. In Chapter 5 we introduce representing matrices of finite essential extensions. Here a normal form for local groups is found by the Gauß algorithm. Uniform groups have representing matrices in Hermite normal form. The classification problems for almost completely decomposable groups up to isomorphism and up to near-isomorphism can be rephrased as equivalence problems for the representing matrices. In Chapter 6 we derive a criterion for the representing matrices of local groups in Gauß normal form. In Chapter 7 we formulate the matrix criterion for uniform groups. Two representing matrices in Hermite normal form describe isomorphic groups if and only if the rest blocks of the representing matrices are T-diagonally equivalent. Starting from a fixed near-isomorphism class in Chapter 8 we investigate isomorphism classes of uniform groups. We count groups and isomorphism classes. In Chapter 9 we specialize on uniform groups of rank 2r with a regulator quotient of rank r such that the rest block of the representing matrix is invertible and normed.},
  subject      = {Fast vollst{\"a}ndig zerlegbare Gruppe},
  language  = {en}
}