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- W2022195670 abstract "Let G be a finite group, p a prime divisor of | G |, and T a p –subgroup of G . Define σ( T ) to be the number of Sylow p –subgroups of G containing T . Call T a central p –Sylow intersection if for some Σ ⊆ Syl p ( G ), T = ∩( S | S є Σ), and if, in addition, T contains the center of a Sylow p –subgroup of G . This work is inspired and motivated by work of G. Stroth [ J. Algebra 37 (1975), 111–120]. Generalizing an argument of his we describe finite groups in which every central p –Sylow intersection T with p –rank( T ) > 2 satisfies σ( T ) ≤ p . Related methods yield the description of finite groups in which every central p –Sylow intersection T with p –rank( T ) ≥ 2 satisfies σ( T ) ≤ 2 p ." @default.
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- W2022195670 date "1977-04-01" @default.
- W2022195670 modified "2023-10-17" @default.
- W2022195670 title "On Sylow intersections" @default.
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- W2022195670 doi "https://doi.org/10.1017/s000497270002325x" @default.
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