Abstract
Abstract
Let p be a prime integer and let
{\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
{\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
\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
\mathrm{SL}_{n}(\mathbb{Z}_{p})
,
Internat. J. Algebra Comput. 20 2010, 8, 1021–1039]
simultaneously.
Funder
Henan Polytechnic University
Education Department of Henan Province
Subject
Applied Mathematics,General Mathematics
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