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A Note on Split Extensions of Finite Groups

Published online by Cambridge University Press:  20 November 2018

Martin R. Pettet
Martin R. Pettet*
Affiliation:
Texas A & M University, College Station, Texas 77843
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Let N and K be finite groups with K acting on N, and let G be the semidirect product NK It was shown by Zassenhaus that if (|N|, |K|) — 1 and either N or K is solvable (an assumption later rendered redundant by the Feit-Thompson theorem), then all complements of N in G are conjugate to K.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 1 , 01 March 1981 , pp. 117 - 119
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Gorenstein, Daniel “Finite Groups,” Harper and Row, New York, 1968.Google Scholar
2. Isaacs, I. M., “Character Theory of Finite Groups,” Academic Press, New York, 1976.Google Scholar