An Application of Subgroup-lattice Theory

YANG YIchuan; Wang Lu

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An Application of Subgroup-lattice Theory

YANG YIchuan *,Wang Lu

Department of Mathematics,Beihang University

*Correspondence author

#Submitted by

Subject:

Funding: %NSFC （No.Grant 11271040）, %and the FRFCU （No.Grant 302996）, Partially supported by the %Research Fund for the Doctoral Program of Higher Education （No.Grant%20091102120045）

Opened online:28 November 2013

Accepted by: none

Citation: YANG YIchuan,Wang Lu.An Application of Subgroup-lattice Theory[OL]. [28 November 2013] http://en.paper.edu.cn/en_releasepaper/content/4569882

It is well-known that a finite group $G$ is cyclic iff $G$ has at most one subgroup of each order dividing $|G|$. There are several proofs of this result. For instance, a popular proof of this theorem is based upon a result of number theory about Euler's totient function. As an application of subgroup lattice theory, we give new proof in this paper.

Keywords:subgroup lattice; finite group; cyclic group

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