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Half-Transitive Automorphism Groups

  • I. M. Isaacs (a1) and D. S. Passman (a1)

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Let G be a finite group and A a group of automorphisms of G. Clearly A acts as a permutation group on G#, the set of non-identity elements of G. We assume that this permutation representation is half transitive, that is all the orbits have the same size. A special case of this occurs when A acts fixed point free on G. In this paper we study the remaining or non-fixed point free cases. We show first that G must be an elementary abelian g-group for some prime q and that A acts irreducibly on G. Then we classify all such occurrences in which A is a p-group.

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Copyright

References

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1. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras (New York, 1962).
2. Roquette, P., Realisierung von Darstellungen endlicher nilpotenter Gruppen, Arch. Math., 9 (1958), 241250.
3. Thompson, J. G., Normal p-complements for finite groups, Math. Z., 72 (1960), 332354.
4. Normal p-complements for finite groups, J. Alg., 1 (1964), 4346.
5. Wielandt, H., Finite permutation groups (New York, 1964).
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Half-Transitive Automorphism Groups

  • I. M. Isaacs (a1) and D. S. Passman (a1)

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