%0 Journal Article
%T On the power graphs of elementary abelian and extra special $p$-groups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Pourhasan, Masoud
%A Doostie, Hossein
%D 2021
%\ 06/01/2021
%V 10
%N 2
%P 89-95
%! On the power graphs of elementary abelian and extra special $p$-groups
%K Power graphs
%K non-group semigroups
%K semidirect product
%R 10.22108/ijgt.2020.120552.1588
%X 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.
%U https://ijgt.ui.ac.ir/article_24531_f2605f3fd1e6973bd072461a34d1e78d.pdf