Let (Formula presented.) be positive integers and (Formula presented.) a class of groups which is closed for subgroups, quotient groups and extensions. Suppose that a finite group G satisfies the condition that for every two subsets M and N of cardinalities m and n, respectively, there exist (Formula presented.) and (Formula presented.) such that (Formula presented.) Then either (Formula presented.) or (Formula presented.).
Applying the Kövári-Sós-Turán theorem to a question in group theory
Lucchini A.
2020
Abstract
Let (Formula presented.) be positive integers and (Formula presented.) a class of groups which is closed for subgroups, quotient groups and extensions. Suppose that a finite group G satisfies the condition that for every two subsets M and N of cardinalities m and n, respectively, there exist (Formula presented.) and (Formula presented.) such that (Formula presented.) Then either (Formula presented.) or (Formula presented.).
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Applying the K v ri S s Tur n theorem to a question in group theory.pdf
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