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A solvability condition for finite groups with nilpotent maximal subgroups

Published online by Cambridge University Press:  17 April 2009

John Randolph
John Randolph
Affiliation:
West Virginia University, Morgantown, West Virginia, USA.
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Abstract

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Let G be a finite group with a nilpotent maximal subgroup S and let P denote the 2-Sylow subgroup of S. It is shown that if P ∩ Q is a normal subgroup of P for any 2-Sylow subgroup Q of G, then G is solvable.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 2 , October 1970 , pp. 273 - 276
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Brauer, Richard and Suzuki, Michio, “On finite groups of even order whose 2-Sylow group is a quaternion group”, Proc. Nat. Aaad. Sci. U.S.A. 45 (1959), 1757–1759.CrossRefGoogle Scholar
[2]Gorenstein, Daniel, Finite groups (Harper's Series in Modern Mathematics, Harper & Row, New York, Evanston, London, 1968).Google Scholar
[3]Janko, Zvonimir, “Finite groups with a nilpotent maximal subgroup”, J. Austral. Math. Soc. 4 (1964), 449–451.CrossRefGoogle Scholar
[4]Randolph, John, “On a theorem of Thompson concerning a class of non-solvable groups”, (to appear).Google Scholar
[5]Scott, W.R., Group theory (Prentice-Hall, Englewood Cliffs, New Jersey, 1964).Google Scholar
[6]Thompson, John G., “Normal p-complements for finite groups”, Math. Z. 72 (1960), 332–354.CrossRefGoogle Scholar