Existence of a Unique group of finite order

Sumit Kumar Upadhyay; Shiv Datt Kumar

Existence of a Unique group of finite order

History and Overview 2011-04-20 v1

Authors: Sumit Kumar Upadhyay , Shiv Datt Kumar

Abstract

Let $n$ be a positive integer. Then cyclic group $Z_n$ of order $n$ is the only group of order $n$ iff g.c.d. $(n,\phi(n))=1$ , where $\phi$ denotes the Euler-phi function. In this article we have given another proof of this result using the knowledge of semi direct product and induction.

Keywords

finite order group cyclic group euler-phi function semi direct product induction

Cite

@article{arxiv.1104.3831,
  title  = {Existence of a Unique group of finite order},
  author = {Sumit Kumar Upadhyay and Shiv Datt Kumar},
  journal= {arXiv preprint arXiv:1104.3831},
  year   = {2011}
}

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