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1968β€’Proceedings of the American Mathematical SocietyOpen access

On finite groups whose 𝑝-Sylow subgroup is a 𝑇.𝐼. set

Henry S. Leonard

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Abstract

Throughoutthis note we let p be a fixed prime and let G he a finite group whose fixed p-Sylow subgroup P is a T. I. set (trivial intersection set).That is, the intersection of any two distinct conjugates of P is (1).Denote \P\ by p".It is conjectured that if G has a faithful complex character % with x(l) =P"I2~1, then PAG.This has been confirmed in certain cases [4, page 287 and Lemma 4.2], [6, Theorem 4.3].In fact under certain conditions it is sufficient to assume x(l) <ipa -1)/2 [l, Theorem 3], [6, Theorem 4.2], but in general the

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Throughoutthis note we let p be a fixed prime and let G he a finite group whose fixed p-Sylow subgroup P is a T. I. set (trivial intersection set).That is, the intersection of any two distinct conjugates of P is (1).Denote \P\ by p".It is conjectured that if G has a faithful complex character % with x(l) =P"I2~1, then PAG.This has been confirmed in certain cases [4, page 287 and Lemma 4.2], [6, Theorem 4.3].In fact under certain conditions it is sufficient to assume x(l) <ipa -1)/2 [l, Theorem 3], [6, Theorem 4.2], but in general the

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Available abstract

Throughoutthis note we let p be a fixed prime and let G he a finite group whose fixed p-Sylow subgroup P is a T. I. set (trivial intersection set).That is, the intersection of any two distinct conjugates of P is (1).Denote \P\ by p".It is conjectured that if G has a faithful complex character % with x(l) =P"I2~1, then PAG.This has been confirmed in certain cases [4, page 287 and Lemma 4.2], [6, Theorem 4.3].In fact under certain conditions it is sufficient to assume x(l) <ipa -1)/2 [l, Theorem 3], [6, Theorem 4.2], but in general the

Key concepts: Sylow theorems, Combinatorics, Mathematics, Set (abstract data type), Finite group, Group (periodic table), Physics, Computer science

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