Abstract
We define the notion of irreducibility of a pgroup and show how any pgroup G can be reduced to an irreducible group H. We show that G is realizable as the Galois group of a regular extension of Q(T) if H is. Finally, we give some sufficient conditions on the number of generators of a pgroup and the structure of its Frattini subgroup for it to be reducible to the trivial group.
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