Can someone please explain the proof of the "Factor group lemma" for Cayley graphs which is stated below.

Factor Group Lemma: Suppose that

1.$N$ is a cyclic, normal subgroup of a group $G$.

2.$(s_1,s_2,\ldots,s_m)$ is a hamiltonian cycle in $Cay(G/N;S)$.

3.The product $s_1s_2\cdots s_m$ generates $N$.

Then $Cay(G;S)$ has a Hamiltonian cycle.

Thanks a lot in advance.

  • $\begingroup$ The formulation is somewhat imprecise (or lacking rigour). It would appear that $S$ is at the same time a subset of both the support set $G$ as well as the quotient-set $G/N$. Perhaps you meant to refer to the image of $S$ under the canonical surjection into the quotient group? The same issue affects the vertices $s_k$. $\endgroup$
    – ΑΘΩ
    Dec 11, 2018 at 7:15
  • $\begingroup$ If anyone knows the name of the text or paper which contains the proof of the above lemma is it possible to mention? I'm asking since I don't have a clear idea about it. Thanks. $\endgroup$ Dec 11, 2018 at 8:04


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