Every finite group is the Fitting quotient of a p-dominated group for any prime p not dividing its order
From Groupprops
History
This result was proved in a paper by Hartley and Robinson.
Statement
Suppose is a finite group and is a prime not dividing the order of . Then, there exists a P-dominated group (?) whose quotient by its Fitting subgroup is .
In other words, there is a Finite complete group (?) (i.e., a finite group that is complete: it is centerless and every automorphism is inner) such that the Fitting subgroup (?) is a group of prime power order for the prime , and the quotient group is isomorphic to . In fact, is the semidirect product of and .
Facts used
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}