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A Hughes-like property for finite groups

Published online by Cambridge University Press:  20 January 2009

R. A. Bryce
Affiliation:
School of Mathematical Sciences, The Australian National University, Canberra, A.C.T. 0200, Australia
V. Fedri
Affiliation:
Dipartimento di Matematica, viale Morgagni, 67/A, 50134 Firenze, Italy
L. Serena
Affiliation:
Dipartimento di Matematica, viale Morgagni, 67/A, 50134 Firenze, Italy
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Abstract

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Several structure theorems are proved for groups G having the following property. There is a prime p and a collection of subgroups of G such that the elements of G which lie in the complement of every subgroup of the collection all have order p.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Bryce, R. A., On a Theorem of Hughes and Thompson, Bull. Austral. Math. Soc. 50 (1994), 4148.Google Scholar
2.Hughes, D. R. and Thompson, J. G., The Hp-problem and the structure of Hp-groups, Pacific J. Math. 9 (1959), 10971101.CrossRefGoogle Scholar
3.Huppert, B., and Blackburn, N., Finite groups (Springer-Verlag, Berlin-Heidelberg-New York, 1982).Google Scholar
4. Otto Kegel, H., Die Nilpotenz der Hp-gruppen, Math. Z. 75 (1961), 373376.Google Scholar
5.Thompson, J. G., Finite groups with fixed point free automorphisms of prime order, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 578581.Google Scholar