Products of nonconjugate maximal subgroups
Jinbao Li, Yong Yang
Abstract
We prove that a finite group G is solvable whenever MN=G for every pair of nonconjugate maximal subgroups M,N<G. Equivalently, every finite nonsolvable group has two nonconjugate maximal subgroups whose setwise product is proper. This gives a negative answer to Problem 10.34 of the Kourovka Notebook. As an application, we also answer an open question raised by Guo.
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