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 and not equal to , then is solvable or . In particular, if the average number of Sylow subgroups of a finite group is , then , where is the largest normal solvable subgroup of . This generalizes an earlier result by Moretó et al.