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## Abstract This is the last in a series of articles where we are concerned with normal elements of noncommutative Iwasawa algebras over SL n ⁢ ( Z p ) {\mathrm{SL}\_{n}(\mathbb{Z}\_{p})} . Our goal in this portion is to give a positive answer to an open question in [D. Han and F. Wei, Normal elements of noncommutative Iwasawa algebras over SL 3 ⁢ ( Z p ) \mathrm{SL}\_{3}(\mathbb{Z}\_{p}) , Forum Math. 31 2019, 1, 111–147] and make 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. Let __n__ ( n ≥ 2 {n\geq 2} ) be a positive integer. Let __p__ ( p > 2 {p>2} ) be a prime integer, Z p {\mathbb{Z}\_{p}} the ring of __p__-adic integers and F p {\mathbb{F}\_{p}} the finite filed of __p__ elements. Let G = Γ 1 ⁢ ( SL n ⁢ ( Z p ) ) {G=\Gamma\_{1}(\mathrm{SL}\_{n}(\mathbb{Z}\_{p}))} be the first congruence subgroup of the special linear group SL n ⁢ ( Z p ) {\mathrm{SL}\_{n}(\mathbb{Z}\_{p})} and Ω G {\Omega\_{G}} the mod-__p__ Iwasawa algebra of __G__ defined over F p {\mathbb{F}\_{p}} . By a purely computational approach, f

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Author

Dong Han; Feng Wei

Publisher

Walter de Gruyter GmbH

Published

2019

Language

EN

Field

Mathematics (Physical Sciences)