English

Normal elements of completed group algebras over ${\rm SL}_3(\mathbb{Z}_p) $

Number Theory 2018-08-21 v1 Group Theory Rings and Algebras

Abstract

Let pp be a prime integer and Zp\mathbb{Z}_p be the ring of pp-adic integers. By a purely computational approach we prove that each nonzero normal element of a completed group algebra over the special linear group SL3(Zp){\rm SL}_3(\mathbb{Z}_p) is a unit. This give a positive answer to an open question in \cite{WeiBian2} and make up for an earlier mistake in \cite{WeiBian1} simultaneously.

Keywords

Cite

@article{arxiv.1802.02676,
  title  = {Normal elements of completed group algebras over ${\rm SL}_3(\mathbb{Z}_p) $},
  author = {Dong Han and Feng Wei},
  journal= {arXiv preprint arXiv:1802.02676},
  year   = {2018}
}