Every finite group is the Fitting quotient of a p-dominated group for any prime p not dividing its order

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


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


Journal references