On some Frobenius groups with the same prime graph as the almost simple group PGL(2,49)

2016/01/02 by Ali Mahmoudifar, Mahmoudifar, Ali
Computer Science · Engineering · Mathematics · #20D05 #20D08 #20D60 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR #msc:20D05 #msc:20D08 #msc:20D60

paper · pdf · doi:10.48550/arxiv.1601.00146

7 pages

arxiv created 2016/01/02 · openalex publication_date 2016/01/02 · arxiv updated 2016/01/05 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

The prime graph of a finite group G is denoted by \ga(G) whose vertex set is π(G) and two distinct primes p and q are adjacent in \ga(G), whenever G contains an element with order pq. We say that G is unrecognizable by prime graph if there is a finite group H with \ga(H)=\ga(G), in while H\not≅ G. In this paper, we consider finite groups with the same prime graph as the almost simple group \textrmPGL(2,49). Moreover, we construct some Frobenius groups whose their prime graph coincide with \ga(\textrmPGL(2,49)), in particular, we get that \textrmPGL(2,49) is unrecognizable by prime graph.

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