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On normally embedded subgroups of locally soluble FC-groups

Published online by Cambridge University Press:  18 May 2009

J. C. Beidleman  and
M. J. Karbe
J. C. Beidleman
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Ky 40506, U.S.A.
M. J. Karbe
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Ky 40506, U.S.A.
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In his Habilitationsschrift [3] B. Fischer introduced the concept of a normally embedded subgroup of a finite group. A subgroup of a finite group G is said to be normally embedded in G if each of its Sylow subgroups is a Sylow subgroup of a normal subgroup of G. Meanwhile this concept has become of considerable importance in the theory of finite soluble groups and has been studied by various authors. However, in infinite group theory, normally embedded subgroups seem to have received little attention. The object of this note is to study normally embedded subgroups of locally soluble FC-groups.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 2 , July 1986 , pp. 153 - 159
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

REFERENCES

1.Anderson, W., Injectors in finite solvable groups, J. Algebra 36 (1975), 333–338.CrossRefGoogle Scholar
2.Chambers, G. A., p-normally embedded subgroups of finite soluble groups J. Algebra 16 (1970), 442–455.CrossRefGoogle Scholar
3.Fischer, B., Klassen konjugierter Untergruppen in endlichen auflösbaren Gruppen, Habilitationsschrift, Universität Frankfurt am Main (1966).Google Scholar
4.Tomkinson, M. J., FC-groups (Pitman, 1984).Google Scholar