Relative Embedding Problems

Authors:
Elena V. Black and John R. Swallow

Journal:
Trans. Amer. Math. Soc. **353** (2001), 2347-2370

MSC (2000):
Primary 12F12, 13B05; Secondary 12F10

DOI:
https://doi.org/10.1090/S0002-9947-00-02625-8

Published electronically:
October 11, 2000

MathSciNet review:
1814073

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider Galois embedding problems such that a Galois embedding problem is solvable, where is a Galois subextension of . For such embedding problems with abelian kernel, we prove a reduction theorem, first in the general case of commutative -algebras, then in the more specialized field case. We demonstrate with examples of dihedral embedding problems that the reduced embedding problem is frequently of smaller order. We then apply these results to the theory of obstructions to central embedding problems, considering a notion of quotients of central embedding problems, and classify the infinite towers of metacyclic -groups to which the reduction theorem applies.

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Additional Information

**Elena V. Black**

Affiliation:
Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019

Address at time of publication:
131 Salina Street, Lafayette, Colorado 80026

Email:
eblack@math.ou.edu

**John R. Swallow**

Affiliation:
Department of Mathematics, Davidson College, Davidson, North Carolina 28036

Email:
joswallow@davidson.edu

DOI:
https://doi.org/10.1090/S0002-9947-00-02625-8

Received by editor(s):
January 4, 1999

Received by editor(s) in revised form:
August 20, 1999

Published electronically:
October 11, 2000

Additional Notes:
The first author gratefully acknowledges a University of Oklahoma Junior Faculty Research Grant. The second author gratefully acknowledges support under National Science Foundation Grant No. DMS-9501366 and a Davidson College MacArthur Faculty Study and Research Grant.

Article copyright:
© Copyright 2000
American Mathematical Society