p-Groups have unbounded realization multiplicity

Details p-Groups have unbounded realization multiplicity p-Groups have unbounded realization multiplicity

2011-09-19

arxiv.org/abs/1109.4070v1

Mathematics

Number Theory

8 pages

Scientific paper

In this paper we interpret the solutions to a particular Galois embedding problem over an extension K/F whose Galois group is a finite, cyclic p group in terms of certain Galois submodules within the parameterizing space of elementary p-abelian extensions of K; here p is a prime. Combined with some basic facts about the module structure of this parameterizing space, this allows us to exhibit a class of p-groups whose realization multiplicity is unbounded.

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