Fields with indecomposable multiplicative groups
نویسندگان
چکیده
منابع مشابه
Indecomposable Linear Groups
Let G be a noncyclic group of order 4, and let K = Z, Z (2) and Z 2 be the ring of rational integers, the localization of Z at the prime 2 and the ring of 2-adic integers, respectively. We describe, up to conjugacy, all of the indecomposable subgroups in the group GL(m, K) which are isomorphic to G. The first explicit description of the Z-representations of the noncyclic group G of order 4 was ...
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This theorem generalizes the (well-known) fact that the multiplicative group of a finite field is cyclic. Most proofs of this fact can actually be used to prove Theorem 1 in all its generality, so there is not much need to provide another proof here. But yet, let us sketch a proof of Theorem 1 that requires only basic number theory. The downside is that it is very ugly. First, an easy number-th...
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Let G be a multiplicative subgroup of the prime field Fp of size |G| > p1−κ and r an arbitrarily fixed positive integer. Assuming κ = κ(r) > 0 and p large enough, it is shown that any proportional subset A ⊂ G contains non-trivial arithmetic progressions of length r. The main ingredient is the Szemerédi-Green-Tao theorem. Introduction. We denote by Fp the prime field with p elements and Fp its ...
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2016
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2015.07.004