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- Title
Normal elements of noncommutative Iwasawa algebras over SL<sub>3</sub>(ℤ_<sub>p</sub>).
- Authors
Han, Dong; Wei, Feng
- Abstract
Let p be a prime integer and let ℤ p {\mathbb{Z}_{p}} be the ring of p-adic integers. By a purely computational approach we prove that each nonzero normal element of a noncommutative Iwasawa algebra over the special linear group SL 3 (ℤ p) {\mathrm{SL}_{3}(\mathbb{Z}_{p})} is a unit. This gives a positive answer to an open question in [F. Wei and D. Bian, Erratum: Normal elements of completed group algebras over SL n (ℤ p) \mathrm{SL}_{n}(\mathbb{Z}_{p}) [mr2747414], Internat. J. Algebra Comput. 23 2013, 1, 215] and makes up for an earlier mistake in [F. Wei and D. Bian, Normal elements of completed group algebras over SL n (ℤ p) \mathrm{SL}_{n}(\mathbb{Z}_{p}) , Internat. J. Algebra Comput. 20 2010, 8, 1021–1039] simultaneously.
- Subjects
PRIME numbers; NONCOMMUTATIVE algebras; IWASAWA theory; CHEVALLEY groups; ABELIAN groups
- Publication
Forum Mathematicum, 2019, Vol 31, Issue 1, p111
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2018-0034