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On a Splitting Theorem of Gaschütz

Published online by Cambridge University Press:  20 January 2009

John S. Rose
John S. Rose
Affiliation:
Peterhouse, Cambridge
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Let G be any finite group, and p any prime number. (All groups to be considered here are finite, and we assume this without further comment.) We denote by Kp(G) the unique smallest normal subgroup of G for which the quotient G/Kp(G) is a p-group. G/Kp(G) is called the p-residual of G. W. Gaschütz (2, Satz 7) has proved the following

Theorem. Set K = Kp(G). If the Sylow p-subgroups of K are abelian, then G splits over K.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 1 , June 1966 , pp. 57 - 60
Copyright
Copyright © Edinburgh Mathematical Society 1966

References

REFERENCES

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