Modules over the Integral Group Ring of a Non-Abelian Group of Order $pq$
Lee Klingler
Jan 1986 · American Mathematical Society: Memoirs of the American Mathematical Society Book 341 · American Mathematical Soc.
Ebook
125
Pages
reportRatings and reviews aren’t verified Learn More
About this ebook
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.
Rate this ebook
Tell us what you think.
Reading information
Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.
