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Some results on the recognizability of the linear groups over the binary field

Mohammad Reza Darafsheh; Yaghoub Farjami; M. Khademi; Ali Reza Moghaddamfar — 2005

Commentationes Mathematicae Universitatis Carolinae

In this paper, we first find the set of orders of all elements in some special linear groups over the binary field. Then, we will prove the characterizability of the special linear group $PSL (13, 2)$ using only the set of its element orders.

A characterization property of the simple group ${PSL}_{4} (5)$ by the set of its element orders

Mohammad Reza Darafsheh; Yaghoub Farjami; Abdollah Sadrudini — 2007

Archivum Mathematicum

Let $ω (G)$ denote the set of element orders of a finite group $G$ . If $H$ is a finite non-abelian simple group and $ω (H) = ω (G)$ implies $G$ contains a unique non-abelian composition factor isomorphic to $H$ , then $G$ is called quasirecognizable by the set of its element orders. In this paper we will prove that the group $P S L_{4} (5)$ is quasirecognizable.

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Some results on the recognizability of the linear groups over the binary field

A characterization property of the simple group PSL 4 ( 5 ) by the set of its element orders

A characterization property of the simple group ${PSL}_{4} (5)$ by the set of its element orders