I am studying papers about " Prime graph" , for example "Prime graph components of finite groups" [ williams], " Groups with complete prime graph connected components" [ Lucido and moghaddanfar]. But I do not understand some of scientific terms in papers to relate this matter. For example, concepts like torus, maximal tori. Can someone explain these terms? How these concepts are used in these articles?
closed as off-topic by Gjergji Zaimi, Andy Putman, Andrey Rekalo, Chris Godsil, Todd Trimble♦ Jun 30 '13 at 1:56
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We know that each torus is a maximal abelian subgroup and so the prime divisors of $|T|$ are mutually adjacent in the prime graph of $G$.
So knowing the order of maximal abelian subgroups of a simple group give many adjacency in the prime graph.
Only one need to determine the adjacency between the characteristic of the field related to the simple group of Lie type to determine the prime graph of a simple group.
I hope that it be helpful.