Title : ( Conjugate Graphs of Finite Groups )
Authors: Ahmad Erfanian , Behnaz Tolue Haghighi ,
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Abstract
In this paper we introduce the conjugate graph Γc G associated to a nonabelian group G with vertex set G\\\\Z(G) such that two distinct vertices join by an edge if they are conjugate. We show if Γc G ∼ Γc S, where S is a finite nonabelian simple group which satisfy Thompson’s conjecture, then G ∼ S. Further, if central factors of two nonabelian groups H and G are isomorphic and |Z(G)| = |Z(H)|, then H and G have isomorphic conjugate graphs.
Keywords
Conjugacy class; nonabelian simple group; conjugate graph
@article{paperid:1032690,
author = {Erfanian, Ahmad and Tolue Haghighi, Behnaz},
title = {Conjugate Graphs of Finite Groups},
journal = {Discrete Mathematics, Algorithms and Applications},
year = {2012},
volume = {4},
number = {2},
month = {June},
issn = {1793-8309},
pages = {35--43},
numpages = {8},
keywords = {Conjugacy class; nonabelian simple group; conjugate graph},
}
%0 Journal Article
%T Conjugate Graphs of Finite Groups
%A Erfanian, Ahmad
%A Tolue Haghighi, Behnaz
%J Discrete Mathematics, Algorithms and Applications
%@ 1793-8309
%D 2012
