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On the power graphs of elementary abelian and extra special $p$-groups | ||
| International Journal of Group Theory | ||
| مقاله 11، دوره 10، شماره 2، شهریور 2021، صفحه 89-95 اصل مقاله (197.17 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2020.120552.1588 | ||
| نویسندگان | ||
| Masoud Pourhasan؛ Hossein Doostie* | ||
| Department of Mathematics, Science and Research Branch Islamic Azad University, Tehran, Iran | ||
| چکیده | ||
| For a given odd prime $p$, we investigate the power graphs of three classes of finite groups: the elementary abelian groups of exponent $p$, and the extra special groups of exponents $p$ or $p^2$. We show that these power graphs are Eulerian for every $p$. As a corollary, we describe two classes of non-isomorphic groups with isomorphic power graphs. In addition, we prove that the clique graphs of the power graphs of two considered classes are complete. | ||
| کلیدواژه‌ها | ||
| Power graphs؛ non-group semigroups؛ semidirect product | ||
| مراجع | ||
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