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Normal complements in finite solvable groups

Published online by Cambridge University Press:  09 April 2009

Donald K. Friesen
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A well known theorem ([1] page 432) in the study of finite groups states that if P is a Sylow p-subgroup of the finite group G, and if P0 is a normal subgroup of P such that whenever two elements, σ and τ, of P are conjugate in G, the cosets σP0 and τP0 are conjugate in P/P0, then there is a normal subgroup K of G such that G = KP and K ∩ P = P0. In this note we will extend this result to allow P to be any Hall subgroup if G is solvable. More precisely, following theorem will be the proved.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 3 , November 1974 , pp. 262 - 264
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Huppert, B., Endliche Gruppen (Springer-Verlag, 1967).CrossRefGoogle Scholar