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Some Remarks on Groups Admitting a Fixed-Point-Free Automorphism

Published online by Cambridge University Press:  20 November 2018

Fletcher Gross
Fletcher Gross*
Affiliation:
University of Alberta, Edmonton, Alberta; University of Utah, Salt Lake City, Utah
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A finite group G is said to be a fixed-point-free-group (an FPF-group) if there exists an automorphism a which fixes only the identity element of G. The principal open question in connection with these groups is whether non-solvable FPF-groups exist. One of the results of the present paper is that if a Sylow p-group of the FPF-group G is the direct product of any number of mutually non-isomorphic cyclic groups, then G has a normal p-complement. As a consequence of this, the conjecture that all FPF-groups are solvable would be true if it were true that every finite simple group has a non-trivial SylowT subgroup of the kind just described. Here it should be noted that all the known simple groups satisfy this property.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1300 - 1307
Copyright
Copyright © Canadian Mathematical Society 1968

References

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