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# On the prime graph of PSL (2, p ) where p > 3 is a prime number

Acta Mathematica Hungarica
Authors: Bahman Khosravi, Behnam Khosravi, and Behrooz Khosravi

## Abstract

Let G be a finite group. We define the prime graph Γ(G) as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, q are joined by an edge if there is an element in G of order pq. Recently M. Hagie [5] determined finite groups G satisfying Γ(G) = Γ(S), where S is a sporadic simple group. Let p > 3 be a prime number. In this paper we determine finite groups G such that Γ(G) = Γ(PSL(2, p)). As a consequence of our results we prove that if p > 11 is a prime number and p ≢ 1 (mod 12), then PSL(2, p) is uniquely determined by its prime graph and so these groups are characterizable by their prime graph.

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# Comparative prime-number theory. I

## Introduction

Acta Mathematica Hungarica
Authors: S. Knapowski and P. Turán
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# Comparative prime-number theory. II

## Comparison of the progressions ≡1 modk and ≡l modk,l≢1 modk

Acta Mathematica Hungarica
Authors: S. Knapowski and P. Turán
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# Comparative prime-number theory. III

## Continuation of the study of comparison of the progressions ≡1 mokk and ≡l modk

Acta Mathematica Hungarica
Authors: S. Knapowski and P. Turán
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# Comparative prime-number theory. IV

## Paradigma to the general case,k=8 and 5

Acta Mathematica Hungarica
Authors: S. Knapowski and P. Turán
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# Comparative prime-number theory. V

## Some theorems concerning the general case

Acta Mathematica Hungarica
Authors: S. Knapowski and P. Turán
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# Comparative prime-number theory. VI

## Continuation of the general case

Acta Mathematica Hungarica
Authors: S. Knapowski and P. Turán
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# Comparative prime-number theory. VII

## The problem of sign-changes in the general case

Acta Mathematica Hungarica
Authors: S. Knapowski and P. Turán
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# Comparative prime-number theory. VIII

## Chebyshev's problem fork=8

Acta Mathematica Hungarica
Authors: S. Knapowsiki and P. Turán
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# On Beurling's prime number theorem

Periodica Mathematica Hungarica
Author: Sz. Gy. Révész
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