Hall Graph of a Finite Group
Abstract
The Hall graph of a finite group is a simple graph whose vertex set is , the set of all prime divisors of its order, and two distinct primes and are joined by an edge if has at least one Hall -subgroup. For all primes of , we call the -tuple , the degree pattern of Hall graph of , where signifies the degree of vertex . This paper provides some properties of Hall graph. It also gives a characterization for some finite simple groups via order and degree pattern of Hall graph.
DOI Code:
10.1285/i15900932v39n2p25
Keywords:
Hall graph; degree pattern of Hall graph; Hall subgroup; simple group
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