Research Article

Solvability and nilpotency of expanded groups relative to the nearring of zero and congruence preserving functions

Published in: Quaestiones Mathematicae
Volume 45 , issue 12 , 2022 , pages: 1965–1976

DOI: 10.2989/16073606.2021.1980918

Author(s): Gary L. Peterson James Madison University, USA , Stuart D. Scott University of Auckland, New Zealand

Keywords: Primary: 16Y30 , Secondary: 08A30 , 08A40 , Expanded group , polynomial function , congruence preserving function , nearring , nearring module

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Abstract

In this paper we study solvability and nilpotency of an expanded group relative to the nearring of zero and congruence preserving functions of the expanded group. A particular case of interest is when the expanded group is a nearring module. This leads to consequences when an expanded group is viewed as a nearring module over its nearring of zero preserving polynomial functions.

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