On the power graphs of elementary abelian and extra special $p$-groups‎

Author(s):

Masoud Pourhasan , Hossein Doostie *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

‎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. 

* The formulas are not displayed correctly.

Keywords:

‎Power graphs‎ , ‎non-group semigroups‎ , ‎semidirect product

Language:
English
Published:
International Journal of Group Theory, Volume:10 Issue: 2, Jun 2021
Pages:
89 to 95
https://magiran.com/p2219896