The p-adic group ring of
The p-adic group ring of
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p-进群环
DOI：
10.1016/j.jalgebra.2014.01.036
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发表时间：
2014
影响因子：
0.9
通讯作者：
F. Eisele
中科院分区：
文献类型：
--
作者：
F. Eisele
在本文中，我们证明了Zp [pf − 1]-阶Zp [pf − 1] SL 2（pf）可以从模p的约简同构于FpfSL 2（pf）的那些阶中识别出来.换句话说，我们证明了F p f SL 2（p f）唯一地提升到Z p [p f− 1]阶，只要对提升施加某些合理的条件。这证明了Nebe在[8]中提出的关于Z2 [<$2 f− 1] SL 2（2 f）的基本阶的猜想。
In the present article we show that the Z p [ζ p f− 1]-order Z p [ζ p f− 1] SL 2 (p f) can be recognized among those orders whose reduction modulo p is isomorphic to F p f SL 2 (p f) using only ring-theoretic properties. In other words we show that F p f SL 2 (p f) lifts uniquely to a Z p [ζ p f− 1]-order, provided certain reasonable conditions are imposed on the lift. This proves a conjecture made by Nebe in [8] concerning the basic order of Z 2 [ζ 2 f− 1] SL 2 (2 f).