Solvability and nilpotency of expanded groups relative to the nearring of zero and congruence preserving functions. Issue 12 (2nd December 2022)

• Record Type: Journal Article
• Authors: Peterson, Gary L.; Scott, Stuart D.
• Is Part Of: Quaestiones mathematicae. Volume 45:Issue 12(2022)
• Page Start: 1965
• Page End: 1976
• Publication Date: 2022-12-02
• Subjects: Primary: 16Y30 -- Secondary: 08A30 -- 08A40; Expanded group -- polynomial function -- congruence preserving function -- nearring -- nearring module; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2021.1980918
• Languages: English
• ISSNs: 1607-3606

Abstract

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.