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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.

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