Udeogu C and Ndubuisi R.U
Keywords: Euler Phi function, generators, cyclic groups, level of a cyclic group, cyclicity degree.
Abstract: Cyclic groups have been characterised in several ways by so many authors over time, but none of these characterizations have been directly in respect of the main ingredient for which the cyclic nature of a group is hinged on; the generator of the group. In this paper therefore, we feel the need to cover this gap, hence, we characterize a cyclic group by the number of its generators. We achieve this by introducing the notion of ‘level of a cyclic group’, denoted group , given a cyclic . With this new characterization, we obtain some important results on cyclic groups up to isomorphism. In addition, we introduce the notion of the ‘cyclicity degree of a cyclic group’ using and then present some non trivial examples to support our main results.
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