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2010 On the minimal ramification problem for semiabelian groups
Hershy Kisilevsky, Danny Neftin, Jack Sonn
Algebra Number Theory 4(8): 1077-1090 (2010). DOI: 10.2140/ant.2010.4.1077

Abstract

It is now known that for any prime p and any finite semiabelian p-group G, there exists a (tame) realization of G as a Galois group over the rationals with exactly d= d(G) ramified primes, where d(G) is the minimal number of generators of G, which solves the minimal ramification problem for finite semiabelian p-groups. We generalize this result to obtain a theorem on finite semiabelian groups and derive the solution to the minimal ramification problem for a certain family of semiabelian groups that includes all finite nilpotent semiabelian groups G. Finally, we give some indication of the depth of the minimal ramification problem for semiabelian groups not covered by our theorem.

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Hershy Kisilevsky. Danny Neftin. Jack Sonn. "On the minimal ramification problem for semiabelian groups." Algebra Number Theory 4 (8) 1077 - 1090, 2010. https://doi.org/10.2140/ant.2010.4.1077

Information

Received: 20 December 2009; Revised: 24 June 2010; Accepted: 1 August 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1221.11218
MathSciNet: MR2832635
Digital Object Identifier: 10.2140/ant.2010.4.1077

Subjects:
Primary: 11R32
Secondary: 20D15

Keywords: Galois group , nilpotent group , ramified primes , semiabelian group , wreath product

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.4 • No. 8 • 2010
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