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Nilpotent groups acting fixed point freely on solvable groups

Published online by Cambridge University Press:  17 April 2009

Beverly J. Bailey
Beverly J. Bailey
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, Minnesota, USA; Department of Pure Mathematics, School of General Studies, Australian National University, Canberra, ACT
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Abstract

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All groups considered are finite. We enlarge the class of groups for which the conjecture below is known to hold, to include all nilpotent groups A such that every proper subgroup of A is Zp ˜ Zp free for all primes p.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 3 , December 1976 , pp. 339 - 346
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Berger, T.R., “Automorphisms of solvable groups”, J. Algebra 27 (1973), 311–340.CrossRefGoogle Scholar
[2]Berger, Thomas R., “Hilpotent fixed point free automorphism groups of solvable groups”, Math. Z. 131 (1973), 305–312.CrossRefGoogle Scholar
[3]Camina, Alan R. and Lockett, F. Peter, “On solvable groups which admit the dihedral group of order eight fixed-point-freely”, Bull. Austral. Math. Soc. 8 (1973), 305–312.CrossRefGoogle Scholar
[4]Gross, Fletcher, “Fixed-point-free operator groups of order 8”, Pacific J. Math. 28 (1969), 357–361.CrossRefGoogle Scholar
[5]Gross, Fletcher, “Elementary abelian operator groups”, Bull. Austral. Math. Soc. 7 (1972), 91–100.CrossRefGoogle Scholar