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On a relation between injectors and certain complemented chief factors of finite soluble groups

Published online by Cambridge University Press:  09 April 2009

A. R. Makan
A. R. Makan
Affiliation:
The University of Alberta, Edmonton, Alberta, Canada
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The Fitting class of finite soluble π-groups, where π is an arbitrary set of primes, has the property that each complement of an -avoided, complemented chief factor of any finite soluble group G contains an -injector of G. In other words, each -avoided, complemented chief factor of G is -complemented in the sense of Hartley (see [2]).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 4 , June 1974 , pp. 385 - 388
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Blessenohl, D. and Gaschütz, W., ‘Über normale Schunck — und Fittingklassen’, Math. Z. 118 (1970), 1–8.CrossRefGoogle Scholar
[2]Hartley, B., ‘On Fischer's dualization of formation theory’, Proc. London Math. Soc. (3) 19 (1969), 193–207.CrossRefGoogle Scholar
[3]Makan, A., ‘Another characteristic conjugacy class of subgroups of finite soluble groups’, J. Austral. Math. Soc. 11 (1970), 395–400.CrossRefGoogle Scholar
[4]Neumann, B. H., ‘Twisted wreath products of groups’, Archiv. Math. 14 (1963), 1–6.CrossRefGoogle Scholar