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A Note on Strongly Closed 2-Subgroups

Published online by Cambridge University Press:  20 November 2018

Paul Fong  and
Morton E. Harris
Paul Fong
Affiliation:
Mathematics Department University of Illinois at Chicago Circle, Chicago, Illinois 60680
Morton E. Harris
Affiliation:
Mathematics Department University of Illinois at Chicago Circle, Chicago, Illinois 60680
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Let T be a Sylow 2-subgroup of the finite group G and let 1<S≤T with S strongly closed in T with respect to G. Let Γ=〈CG(s), NG(Ω1(S))| s∊I(S)〉. Suppose that Γ≤H<G for some subgroup H of G. Then H∩〈SG〉 is strongly embedded in 〈SG〉 and S=T∩〈SG〉 or S=Ω1(T∩〈SG〉). Also if m(S) = 1, then S=T∩〈SG〉.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 1 , 01 March 1980 , pp. 99 - 101
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Aschbacher, M., On finite groups of component type, Illinois J. Math. 19 (1975), 87-115.Google Scholar
2. Goldschmidt, D., 2-fusion in finite groups, Annals of Math. 99 (1974), 70-117.Google Scholar
3. Goldschmidt, D., Strongly closed 2-subgroups of finite groups, Annals of Math. 102 (1975), 475-89.Google Scholar