Groupprops, The Group Properties Wiki (pre-alpha)

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Contents 1 History 2 Statement 3 Facts used 4 References 4.1 Journal references

History

This result was proved in a paper by Hartley and Robinson.

Statement

Suppose H is a finite group and p is a prime not dividing the order of H. Then, there exists a p-dominated group whose quotient by its Fitting subgroup is H.

In other words, there is a finite complete group G (i.e., a finite group that is complete: it is centerless and every automorphism is inner) such that the Fitting subgroup F(G) is a group of prime power order for the prime p, and the quotient group G / F(G) is isomorphic to H. In fact, G is the semidirect product of F(G) and H.

Facts used

1. Bryant-Kovacs theorem

References

Journal references

• On finite complete groups by Brian Hartley and Derek John Scott Robinson, Archiv der Mathematik, ISSN 1420-8938 (Online), ISSN 0003-889X (Print), Volume 35,Number 1, Page 67 - 74(Year 1980): ^{PDF copy (Springerlink)More info}