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P-class towers of imaginary quadratic fields [microform]
Bib ID 3416988
Format MicroformMicroform, BookBook
Author
Bush, Michael Raymond
 
Description 73 p. 
Summary

Let k be an imaginary quadratic field and p an integer prime. Let knr,p be the maximal unramified p-extension of k and G = Gal (knr,p/k) the associated pro-p Galois group. We use the p-group generation algorithm to show that G is finite in several cases where this was unknown previously. In particular in the case p = 2 we resolve a question of Stark's regarding the field Q-2379 and show that a criterion (on the infinitude of G) due to Hajir cannot be sharpened. We also exhibit the first examples of fields for which G is a finite 2-group with derived length >2, and begin a survey of those finite 2-groups which arise when k has small discriminant. Next we compute G for several imaginary quadratic fields when p = 3 extending some earlier work of Scholz and Taussky. For an arbitrary odd prime we show how work of Koch and Venkov implies that G is never metacyclic, except when it is already cyclic.

We also give explicit descriptions of two families of groups that arose during our investigations and that have conjecturally several interesting properties. We conclude with a preliminary description of some joint work with Nigel Boston on the asymptotic distributions of non-abelian G with respect to the discriminant.

Notes

(UnM)AAI3130888

Adviser: Nigel Boston.

Source: Dissertation Abstracts International, Volume: 65-04, Section: B, page: 1891.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.

Reproduction Microfiche. Ann Arbor, Mich.: University Microfilms International. 
Subjects Mathematics.
Other authors/contributors University of Illinois at Urbana-Champaign

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