Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-14T17:54:27.340Z Has data issue: false hasContentIssue false

A Characteristic Subgroup of π-Stable Groups

Published online by Cambridge University Press:  20 November 2018

Zvi Arad*
Affiliation:
Tel Aviv University, Tel Aviv, Israel
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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), 11011135.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) 7751029.Google Scholar
5. Hall, P., Theorems like Sylow's, Proc. London Math. Soc. 6 (1956), 286304.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), 554558.Google Scholar