Computation of several cyclotomic Swan subgroups
Authors:
Timothy Kohl and Daniel R. Replogle
Journal:
Math. Comp. 71 (2002), 343348
MSC (2000):
Primary 11R33, 11R18
Published electronically:
October 18, 2000
MathSciNet review:
1863005
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Abstract: Let denote the locally free class group, that is the group of stable isomorphism classes of locally free modules, where is the ring of algebraic integers in the number field and is a finite group. We show how to compute the Swan subgroup, , of when , a primitive th root of unity, , where is an odd (rational) prime so that and 2 is inert in We show that, under these hypotheses, this calculation reduces to computing a quotient ring of a polynomial ring; we do the computations obtaining for several primes a nontrivial divisor of These calculations give an alternative proof that the fields for =11, 13, 19, 29, 37, 53, 59, and 61 are not HilbertSpeiser.
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 C. Greither, D. R. Replogle, K. Rubin, and A. Srivastav, Swan Modules and HilbertSpeiser Number Fields, J. Number Theory, 79 (1999), 164173. CMP 2000:04
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 D. R. Replogle, Swan Classes and Realisable Classes for Integral Group Rings over Groups of Prime Order, Thesis, SUNY Albany, 1997.
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 D. R. Replogle, Cyclotomic Swan Subgroups and Irregular Indices, Rocky Mountain J. Math. (to appear).
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 A. Srivastav, Galois Module Structure Subfileds of tame extensions of and adic functions, submitted for publication.
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 A. Srivastav and S. Venkataraman, Relative Galois module structure of quadratic extensions, Indian J. Pure. Appl. Math., 25 No. 5 (1994), 473488. MR 95c:11133
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Additional Information
Timothy Kohl
Affiliation:
Office of Information Technology, Boston University, Boston, Massachusetts
Email:
tkohl@math.bu.edu
Daniel R. Replogle
Affiliation:
Department of Mathematics and Computer Science, College of Saint Elizabeth, Morristown, New Jersey
Email:
dreplogle@liza.stelizabeth.edu
DOI:
http://dx.doi.org/10.1090/S0025571800013028
PII:
S 00255718(00)013028
Received by editor(s):
August 14, 1998
Received by editor(s) in revised form:
March 1, 2000
Published electronically:
October 18, 2000
Article copyright:
© Copyright 2000 American Mathematical Society
