FINITE GROUPS ADMITTING A FIXED-POINT-FREE AUTOMORPHISM OF ORDER 4.*

@article{Gorenstein1961FINITEGA,
  title={FINITE GROUPS ADMITTING A FIXED-POINT-FREE AUTOMORPHISM OF ORDER 4.*},
  author={Daniel Gorenstein and Israel N. Herstein},
  journal={American Journal of Mathematics},
  year={1961},
  volume={83},
  pages={71}
}
Recently, in a remarkable piece of work [4, 5] John Thompson has proved a result which implies as an immediate corollary the well-known Frobenius conjecture, namely that a finite group admitting a fixed-point-free automorphism (i. e., leaving only the identity element fixed) of prime order must be nilpotent. However, non-nilpotent groups are known which admit fixedpoint-free automorphisms of composite order. In all these cases one notices that the groups in question are solvable. Although the… 

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  • Mathematics
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  • 1969
Let G denote a finite group with a fixed-point-free automorphism of prime order p. Then it is known (see [3] and [8]) that G is nilpotent of class bounded by an integer k(p). From this it follows

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In the course of investigating the structure of finite groups which have a representation in the form ABA, for suitable subgroups A and B, we have been forced to study groups G which admit an

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

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