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A new characterization of Janko simple groups
AIMS Mathematics 2024, 9(4): 9587-9596
Published: 15 April 2024
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In this paper, we studied the influence of centralizers on the structure of groups, and demonstrated that Janko simple groups can be uniquely determined by two crucial quantitative properties: its even-order components of the group and the set π p m ( G ). Here, G represents a finite group, π ( G ) is the set of prime factors of the order of G, p m is the largest element in π ( G ), and π p m ( G ) = { | C G ( x ) | | x G and | x | = p m } denotes the set of orders of centralizers of p m -order elements in G.

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