A note on simple trinomial units in $U_{1}(\mathbb{Z}C_{p})$

Authors: NECAT GÖRENTAŞ

Abstract: In this paper, some new notions are defined about the unit group $U_{1}(\mathbb{Z}G)$ of a finite group G. Especially, notion of simple unit is defined by using the number of elements in its support and absolutely small coefficients of the unit. Units are classified as monomial, binomial, trinomial and k-nomial, level, unit with level $l$ and simple unit. We have shown triviality of monomial units and nonexistence of binomial units in the unit group $U_{1}(\mathbb{Z}G)$ of an arbitrary finite group G. Some basic results and examples are posed about simple units and simple trinomial units in $U_{1}(\mathbb{Z}C_{p})$of a cyclic group $C_{p}$, where $p\geqslant5$.

Keywords: Monomial unit, binomial unit, trinomial unit, unit with level $l$, simple unit

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