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On a special class of finite 2-groups

Published online by Cambridge University Press:  18 May 2009

Marian Deaconescu
Marian Deaconescu
Affiliation:
Department of MathematicsUniversity of Timisoara, Romania
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In the course of classifying those finite groups F which have exactly five maximal subgroups, R. W. van der Waall [4] proved that one encounters the following situation. One class of such groups F is described by F = SP, where S = O2(F)∈Syl2(F), P ∈ Syl3(F), S/Φ(S) ≅ Z2 × Z2, P is cyclic and P operates via conjugation on 5 as a group of order 3, because in this case F/Φ(F) ≅ A4.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 1 , January 1992 , pp. 127 - 131
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Gorenstein, D., Finite groups (Harper & Row, 1968).Google Scholar
2.Hall, M. and Senior, J. K., The Groups of Order 2n (n ≤ 6) (Macmillan, 1964).Google Scholar
3.Martin, U., Almost all p-groups have automorphism group a p-group, Bull. A.M.S. 15 (1) (1986), 78–82.CrossRefGoogle Scholar
4.van der Waall, R. W., Finite groups with m maximal subgroups, m ≤ 7, Stevin, Simon, 50, 1 (1976), 23–40.Google Scholar