ABELIAN F.P.F. OPERATOR GROUPS OF TYPE (p, p)

@inproceedings{Richards2010ABELIANFO,
  title={ABELIAN F.P.F. OPERATOR GROUPS OF TYPE (p, p)},
  author={James W. Richards},
  year={2010}
}
A group A of automorphisms on a group G is said to be fixed-point-free, written f.p.f., if CoiA) = {g&G\ga-g for all «Gi }=7 It has been shown by E. Shult that if A is an abelian f.p.f coprime group of automorphisms of order n=pil • • • pfyon a solvable group G, then the nilpotent length of G is bounded above by <p{n) = 2~LÍ-i a< unless |G| is divisible by primes q suchthat q" + l =d where d divides the exponent e of A. F. Gross has removed the exceptional condition on the prime divisors of \G… 

References

SHOWING 1-6 OF 6 REFERENCES
SOLVABLE GROUPS ADMITTING A FIXED-POINT-FREE AUTOMORPHISM OF PRIME POWER ORDER
Here h(G), the Fitting height (also called the nilpotent length) of G, is as defined in [7]. 1I(G), the r-length of G, is defined in an obvious analogy to the definition of p-length in [2]. Higman
On groups admitting fixed point free abelian operator groups
Endliche Gruppen I