Algebra & Number Theory
- Algebra Number Theory
- Volume 4, Number 8 (2010), 1077-1090.
On the minimal ramification problem for semiabelian groups
It is now known that for any prime and any finite semiabelian -group , there exists a (tame) realization of as a Galois group over the rationals with exactly ramified primes, where is the minimal number of generators of , which solves the minimal ramification problem for finite semiabelian -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 . Finally, we give some indication of the depth of the minimal ramification problem for semiabelian groups not covered by our theorem.
Algebra Number Theory, Volume 4, Number 8 (2010), 1077-1090.
Received: 20 December 2009
Revised: 24 June 2010
Accepted: 1 August 2010
First available in Project Euclid: 20 December 2017
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Kisilevsky, Hershy; Neftin, Danny; Sonn, Jack. On the minimal ramification problem for semiabelian groups. Algebra Number Theory 4 (2010), no. 8, 1077--1090. doi:10.2140/ant.2010.4.1077. https://projecteuclid.org/euclid.ant/1513729610