Torsion completeness of p-primary components in modular group rings of p-reduced Abelian groups

Peter Danchev

doi:10.1007/s10998-009-9037-x

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 59: Issue 1

Torsion completeness of p-primary components in modular group rings of p-reduced Abelian groups

Author:

Peter Danchev

Peter Danchev 13, General Kutuzov Street, bl. 7, fl. 2, ap. 4 4003 Plovdiv Bulgaria

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Pages:: 37–42

Online Publication Date:: 17 Sep 2009

Publication Date:: 01 Sep 2009

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s10998-009-9037-x

Keywords:: 16U60; 16S34; 20K10; 20K21; torsion-complete groups; p-reduced groups; p-mixed groups; group rings; normalized units; Cauchy sequences; nilpotents; bounded groups

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Abstract

Let G be a p-reduced Abelian group and R a commutative unital ring of prime characteristic p such that for each natural number i the subring

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$R^{p^i }$$ \end{document}

has nilpotent elements. It is shown that if S(RG) is the normalized Sylow p-group in the group ring RG, then S(RG) is torsion-complete if and only if G is a bounded p-group. This strengthens our former results on this subject.

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)