Normalp-complements for finite groups

@article{Thompson1959NormalpcomplementsFF,
  title={Normalp-complements for finite groups},
  author={John G. Thompson},
  journal={Mathematische Zeitschrift},
  year={1959},
  volume={72},
  pages={332-354}
}
The minimal number of generators of the group Q is denoted m(s). We define d(B) = max m(s) where ‘21 ranges over all the abelian subgroups of EJ and we let J(cli) be the subgroup generated by all the abelian subgroups ‘u of (5 which satisfy d(B) = m(a). Clearly, if J(S) c R c Q, then J(B) is a characteristic subgroup of R, J(B) char Ji. Z(G) denotes the center of 8 and / 0, jr, is the order of a SD-subgroup of Q. 

Normal p-complements for finite groups

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References

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Theory of Groups of Finite Order

Preface to the second edition Preface to the first edition 1. On permutations 2. The definition of a group 3. On the simpler properties of a group which are independent of its mode of representation

The Theory Of Groups

Introduction Normal subgroups and homomorphisms Elementary theory of abelian groups Sylow theorems Permutation groups Automorphisms Free groups Lattices and composition series A theorem of Frobenius

The theory of groups

FINITE GROUPS WITH FIXED-POINT-FREE AUTOMORPHISMS OF PRIME ORDER.

  • J. Thompson
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1959