arXiv subjects

Alireza Moghaddamfar

Publications and source records attributed to Alireza Moghaddamfar.

3 recordsLinked to original sources

arXiv2018

Some properties of various graphs associated with finite groups

In this paper we have investigated some properties of the power graph and commuting graph associated with a finite group, using their tree-numbers. Among other things, it has been shown that the simple group $L_2(7)$ can be characterized through the tree-number of its power graph. Moreover, the classification of groups with power-free decomposition is presented. Finally, we have obtained an explicit formula concerning the tree-number of commuting graphs associated with the Suzuki simple groups.

math.GR↗

arXiv2018

An OD-Characterizable Class of Simple Groups

It is proved that finite nonabelian simple groups $S$ with $\max π(S)=37$ are uniquely determined by their order and degree pattern in the class of all finite groups.

math.GR↗

arXiv2015

Recognizing by Spectrum for the Automorphism Groups of Sporadic Simple Groups

The spectrum of a finite group is the set of its element orders, and two groups are said to be isospectral if they have the same spectra. A finite group $G$ is said to be recognizable by spectrum, if every finite group isospectral with $G$ is isomorphic to $G$. We prove that if $S$ is any of the sporadic simple groups $M^cL$, $M_{12}$, $M_{22}$, $He$, $Suz$, $O'N$, then ${\rm Aut}(S)$ is recognizable by spectrum. This finishes the proof of the recognizability by spectrum of the automorphism groups of all sporadic simple groups, except $J_2$. Furthermore, we show that if $G$ is isospectral with ${\rm Aut}(J_2)$, then either $G$ is isomorphic to ${\rm Aut}(J_2)$, or $G$ is an extension of a $2$-group by $\mathbb{A}_8$.

math.GR↗