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A Characteristic Subgroup of π-Stable Groups

Published online by Cambridge University Press:  20 November 2018

Zvi Arad
Zvi Arad*
Affiliation:
Tel Aviv University, Tel Aviv, Israel
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All groups in this paper are assumed to be finite.

Let G be a group with op(G) ≠ 1 which is p-constrained and p-stable, p odd. If P is an Sp-subgroup of G, then by Glaubermaris Theorem, [3, 8.2.11],

G = Op′(G)NG(ZJ(P)).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1509 - 1514
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Arad, Z. and Glauberman, G., A characteristic subgroup of a group of odd order (to appear).Google Scholar
2. Glauberman, G., A characteristic subgroup of a p-stable group. Can. J. Math. 20 (1968), 1101–1135.Google Scholar
3. Gorenstein, D., Finite groups (Harper and Row, New York, 1968).Google Scholar
4. Feit, W. and Thompson, J. G., Solvability of groups of odd order, Pacific J. Math. 13 (1963) 775–1029.Google Scholar
5. Hall, P., Theorems like Sylow's, Proc. London Math. Soc. 6 (1956), 286–304.Google Scholar
6. Huppert, B., Endliche Gruppen, I (Springer-Verlag, New York, 1967).Google Scholar
7. Mann, A., Injectors of finite groups, Israel J. Math. 9 (1971), 554–558.Google Scholar