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arXiv · 1201.3875

p-Group Camina pairs

Mark L. Lewis
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Abstract

Let $(G,Z(G))$ be a Camina pair. We prove that $G$ must be a $p$-group for some prime $p$. We also prove that $|Z(G)| < |G:Z(G)|^{3/4}$. Also, we discuss how one might build examples with $|Z(G)| > |G:Z(G)|^{1/2}$, although we are not able to prove the existence of such examples.

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Mark L. Lewis. 2012-01-18. p-Group Camina pairs. https://doi.org/10.1515/jgt-2012-0010

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