On finite groups with prescribed two-generator subgroups and integral Cayley graphs

Yan-Quan Feng; István Kovács

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arXiv · 2104.00434

On finite groups with prescribed two-generator subgroups and integral Cayley graphs

Yan-Quan Feng·István Kovács

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Abstract

In this paper, we characterize the finite groups $G$ of even order with the property that for any involution $x$ and element $y$ of $G$, $\langle x, y \rangle$ is isomorphic to one of the following groups: $\mathbb{Z}_2,$ $\mathbb{Z}_2^2$, $\mathbb{Z}_4$, $\mathbb{Z}_6$, $\mathbb{Z}_2 \times \mathbb{Z}_4$, $\mathbb{Z}_2 \times\mathbb{Z}_6$ and $A_4$. As a result, a characterization will be obtained for the finite groups all of whose Cayley graphs of degree $3$ have integral spectrum.

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BibTeX RIS

Yan-Quan Feng, István Kovács. 2021-04-01. On finite groups with prescribed two-generator subgroups and integral Cayley graphs. https://arxiv.org/abs/2104.00434

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