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Structure theorems for groups with dihedral 3-normalisers

Published online by Cambridge University Press:  20 January 2009

N. K. Dickson
N. K. Dickson
Affiliation:
University of Glasgow, Department of Mathematics, University Gardens, Glasgow, Scotland, G12 8QW.
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In this paper we prove five structure theorems for groups with dihedral 3-normalisers. The interest in these theorems lies not so much in the results themselves as in what can be proved from them. The original versions of the results are contained in our doctoral thesis (1) where they are used to prove the following theorem, of which this paper, together with (2), (3) and other papers in preparation, will constitute a published proof:

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , Issue 2 , September 1978 , pp. 175 - 186
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

REFERENCES

(1) Dickson, N. K., D.Phil, thesis, University of Oxford (1975).Google Scholar
(2) Dickson, N. K., Conjugacy in groups with dihedral 3-normalisers, Glasgow Math. J. 18 (1977), 167–173.CrossRefGoogle Scholar
(3) Dickson, N. K., 2-groups normalized by SL(2,2”), J. Algebra 47 (1977), 529–546.CrossRefGoogle Scholar
(4) Gorenstein, D., Finite groups (Harper and Row, New York, 1968).Google Scholar
(5) Hall, M. JR., and Senior, J., The groups of order 2n (n ≤ 6) (Macmillan, New York, 1964).Google Scholar
(6) Higman, G., Suzuki 2-groups, Illinois J. Math. 7 (1963), 79–96.CrossRefGoogle Scholar
(7) Shult, E. E., On groups admitting fixed-point-free abelian operator groups, Illinois J. Math. 9 (1965), 701–720.CrossRefGoogle Scholar
(8) Stewart, W. B., D. Phil, thesis, University of Oxford (1967).Google Scholar
(9) Stewart, W. B., Groups having strongly self-centralizing 3-centralizers, Proc. London Math. Soc. (3) 26 (1973), 653–680.CrossRefGoogle Scholar