6533b7d6fe1ef96bd126651e

RESEARCH PRODUCT

The average number of Sylow subgroups of a finite group

Alexander Moretó

subject

p-groupDiscrete mathematicsFinite groupComplement (group theory)General MathematicsSylow theoremsMathematics::Algebraic TopologyHall subgroupCombinatoricsMathematics::Group TheoryNormal p-complementLocally finite groupComponent (group theory)Mathematics

description

We prove that if the average Sylow number (ignoring the Sylow numbers that are one) of a finite group G is ⩽7, then G is solvable.

https://doi.org/10.1002/mana.201300064