Notes on the minimal number of ramified primes in some l-extensions of Q

摘要

For a finite l-group G, let ram(t)(G) denote the minimal integer such that G can be realized as the Galois group of a tamely ramified extension of Q ramified only at ram(t)(G) finite primes. We study the upper bound of ram(t)(G) and give an improvement of the result of Plans. We also give the best bound of ram(t)(G) for all 3-groups G of order less than or equal to 3(5).