Displaying similar documents to “Структура пересечений нильпотентных π -подгрупп в π -разрешимых конечных группах”

Notes on the average number of Sylow subgroups of finite groups

Jiakuan Lu, Wei Meng, Alexander Moretó, Kaisun Wu (2021)

Czechoslovak Mathematical Journal

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We show that if the average number of (nonnormal) Sylow subgroups of a finite group is less than 29 4 then G is solvable or G / F ( G ) A 5 . This generalizes an earlier result by the third author.

On the average number of Sylow subgroups in finite groups

Alireza Khalili Asboei, Seyed Sadegh Salehi Amiri (2022)

Czechoslovak Mathematical Journal

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We prove that if the average number of Sylow subgroups of a finite group is less than 41 5 and not equal to 29 4 , then G is solvable or G / F ( G ) A 5 . In particular, if the average number of Sylow subgroups of a finite group is 29 4 , then G / N A 5 , where N is the largest normal solvable subgroup of G . This generalizes an earlier result by Moretó et al.

On TI-subgroups and QTI-subgroups of finite groups

Ruifang Chen, Xianhe Zhao (2020)

Czechoslovak Mathematical Journal

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Let G be a group. A subgroup H of G is called a TI-subgroup if H H g = 1 or H for every g G and H is called a QTI-subgroup if C G ( x ) N G ( H ) for any 1 x H . In this paper, a finite group in which every nonabelian maximal is a TI-subgroup (QTI-subgroup) is characterized.