关于半交换群的极小分歧问题
On the minimal ramification problem for semiabelian groups
摘要：
对任意素数p和有限半交换p-群G，存在G作为有理数Q上的伽罗瓦群的一个（驯服）实现，其中d = d（G）是G的最小生成元个数，解决了有限半交换p-群的最小分歧问题.我们推广了这个结果，得到了关于有限半交换群的一个定理，并得到了包含所有有限幂零半交换群G的一类半交换群的极小分歧问题的解.最后，我们给出了一些指示的深度的最小分歧问题的半交换群不包括我们的定理。
英文摘要：
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 Q 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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