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Characterisations of Galois extensions of prime cubed degree

Published online by Cambridge University Press:  17 April 2009

James E. Carter
James E. Carter
Affiliation:
Department of Mathematics, College of Charleston, Charleston SC 29424–0001, United States of America, e-mail: carter@math.cofc.edu
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Abstract

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Let p be a prime number and let k be a field of characteristic not equal to p. Assuming k contains the appropriate roots of unity, we characterise the non-cyclic Galois extensions of k of degree p3. Concrete examples of such extensions are given for each possible case which can occur, up to isomorphism.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 1 , February 1997 , pp. 99 - 112
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Carter, J.E., Steinitz classes of tamely ramified nonabelian extensions of algebraic number fields of degree p3, Ph.D. Thesis (Dept. of Mathematics, University of Illinois at Urbana–Champaign, 1992).Google Scholar
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