Abstract
Let N be a normal subgroup of a group G and let p be a prime. We prove that if the p-part of |x|G is a constant for every prime-power order element x ∈ N∖Z(N), then N is solvable and has normal p-complement.
Funding source: Valencian Government
Award Identifier / Grant number: PROMETEO/2011/30
Funding source: Spanish Government
Award Identifier / Grant number: MTM2010-19938-C03-02
Funding source: NNSF of China
Award Identifier / Grant number: 11201401
Funding source: NNSF of China
Award Identifier / Grant number: 11301218
Funding source: University of Jinan Research Funds for Doctors
Award Identifier / Grant number: XBS1335
Funding source: University of Jinan Research Funds for Doctors
Award Identifier / Grant number: XBS1336
C. G. Shao wants to express his deep gratitude for the warm hospitality he has received in the Departamento de Matemáticas of the Universidad Jaume I in Castellón, Spain.
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