In this paper, we consider regular automorphism groups of graphs in the RT$2$ family and the Davis-Xiang family and amorphic abelian Cayley schemes from these graphs. We derive general results on the existence of non-abelian regular automorphism groups from abelian regular automorphism groups and apply them to the RT$2$ family and Davis-Xiang family and their amorphic abelian Cayley schemes to produce amorphic non-abelian Cayley schemes.

中文翻译：

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非阿贝尔 2 群中的偏差分集和非晶凯莱方案

在本文中，我们考虑了 RT$2$ 族和 Davis-Xiang 族中图的规则自同构群以及来自这些图中的非晶阿贝尔凯莱方案。我们从阿贝尔正则自同构群中推导出非阿贝尔正则自同构群存在的一般结果，并将它们应用到 RT$2$ 族和 Davis-Xiang 族及其非晶阿贝尔凯莱方案，以产生非晶非阿贝尔凯莱方案。