Finite p-groups and k((t))

JOURNAL OF ALGEBRA

卷:344

Article

Bevelacqua, Anthony J.¹ 

[1] Univ N Dakota, Dept Math, Grand Forks, ND 58202 USA

关键词: p-Groups;    Laurent series;   

DOI  :  10.1016/j.jalgebra.2011.08.002

来源: Elsevier

【 摘 要 】

Let k be a field of characteristic p > 0 and let K = k((t)) be the field of Laurent series over k. For each group G of order p(n) there exist units u is an element of k[t] such that K/k((ut(Pn))) is Galois with Gal(K/k((ut(Pn)))) congruent to G. We explore the connections between G and u. Among other results, we prove that if both K/k((u(1)(tPn))) and K/k((u(2)(tPn))) are Galois and u(1) and u(2) are sufficiently close in the t-adic topology, then Gal(K/k((u(1)(tPn)))) congruent to Gal(K/k((u(2)(tPn)))). (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free