##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Danny Neftin

#### The Technion, Haifa, Israel

## On the Minimal Ramification Problem for Semiabelian Groups

##### Abstract:

Let G be a finite group and d(G) the minimal number of conjugacy classes that generate G. In any tame realization of G as a Galois group over Q there are at least d(G) ramified primes. The (tame) minimal ramification problem asks whether any group G can be realized (tamely) over Q with exactly d(G) ramified primes. It has been recently proved that this problem has an affirmative answer for a substantial class of finite nilpotent groups (all finite semiabelian nilpotent groups). (Joint work with Hershy Kisilevsky and Jack Sonn)

Host: Cristian Popescu

### November 4, 2010

### 2:00 PM

### AP&M 7321

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