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NILPOTENCY OF THE GROUP OF UNITS OF A FINITE RING

Part of: Chain conditions, growth conditions, and other forms of finiteness

Published online by Cambridge University Press:  26 February 2009

DAVID DOLŽAN
DAVID DOLŽAN*
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 21, Ljubljana 1000, Slovenia (email: [email protected])
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Abstract

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In this paper we find all finite rings with a nilpotent group of units. It was thought that the answer to this was already given by McDonald in 1974, but as was shown by Groza in 1989, the conclusions that had been reached there do not hold. Here, we improve some results of Groza and describe the structure of an arbitrary finite ring with a nilpotent group of units, thus solving McDonald’s problem.

Keywords

finite ringgroup of unitsnilpotent

MSC classification

Secondary: 16P10: Finite rings and finite-dimensional algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 2 , April 2009 , pp. 177 - 182
Copyright
Copyright © Australian Mathematical Society 2009

References

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