Good action of a nilpotent group with regular orbits

@article{Ercan2021GoodAO,
  title={Good action of a nilpotent group with regular orbits},
  author={G{\"u}lin Ercan and İsmail Ş. G{\"u}loğlu},
  journal={Communications in Algebra},
  year={2021},
  volume={50},
  pages={4191 - 4194}
}
Abstract Suppose that A is a finite nilpotent group of odd order having a good action, in the sense of [1], on the group G of odd order. Under some additional assumptions we prove that the Fitting height of G is bounded above by the sum of the numbers of primes dividing and counted with multiplicities. 

References

SHOWING 1-6 OF 6 REFERENCES

Regular orbits on symplectic modules

Characters and blocks of finite groups

Preface 1. Algebras 2. Brauer characters 3. Blocks 4. The first main theorem 5. The second main theorem 6. The third main theorem 7. The Z*-theorem 8. Brauer characters as characters 9. Blocks and

Groups of automorphisms and centralizers

  • A. Turull
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1990
Let G be a finite solvable group and A a group of automorphisms of G such that (|A|, |G|) = 1. We denote by h(G) the Fitting height of G and by l(A) the length of the longest chain of subgroups of A.

Good action on a finite group

Extensions of several coprime results to good action case

Let [Formula: see text] and [Formula: see text] be groups where [Formula: see text] acts on [Formula: see text] by automorphisms. We say “the action of[Formula: see text] on[Formula: see text] is