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  • Modules over the integral group ring of a non-abelian group of order pq
    Klingler, Lee, 1955-
    If ▫$p,q$▫ are primes with ▫$p\equiv 1$▫ ▫$({\rm mod}\,q)$▫ there is a unique nonabelian group ▫$G$▫ of order ▫$pq$▫. The author obtains a classification of the finitely generated ▫$ZG$▫-modules in ... sufficient detail to show (1) the Krull-Schmidt theorem fails but the number of indecomposable summands of a decomposable module is independent of the decomposition. He determines (2) the extent to which cancellation of direct summands ▫$(A\oplus B\approx A\oplus C$▫ implying ▫$B\approx C)$▫ is valid. He finds (3) the obstruction (in an appropriate semigroup) to the isomorphism of two modules which have isomorphic $t$-adic completions for each prime ▫$t$▫. The indecomposable modules are constructed by expressing the ring $ZG$ as a pull-back.
    Vrsta gradiva - knjiga
    Založništvo in izdelava - Providence : American Mathematical Society, cop. 1986
    Jezik - angleški
    ISBN - 0-8218-2343-4
    COBISS.SI-ID - 2841177

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