Classification of finite Cθθ-groups with even order and its application

2017/03/02 by Ali Mahmoudifar, Mahmoudifar, Ali
Engineering · Mathematics · #20D05 #20D08 #20D60 #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.1703.00635

7 pages

arxiv created 2017/03/02 · openalex publication_date 2017/03/02 · arxiv updated 2017/03/03 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

A finite group of order divisible by 3 in which centralizers of 3-elements are 3-subgroups will be called a Cθθ-group. The prime graph (or Gruenberg-Kegel graph) of a finite group G is denoted by Γ(G) (or GK(G)) and its a familiar. Also the degrees sequence of Γ(G) is called the degree pattern of G and is denoted by D(G). In this paper, first we classify the finite Cθθ-groups with even order. Then we show that there are infinitely many Cθθ-groups with the same degree pattern. Finally, we proved that the simple group PSL(2, q) and the almost simple group PGL(2, q), where q > 9 is a power of 3, are determined by their degree pattern.

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