Abstract
Hawkes showed in [10] that classes of metanilpotent groups which are both formations and Fitting classes are saturated and subgroup closed; more, he characterized all such classes as those local formations with a local definition consisting of saturated formations (of nilpotent groups). In [3] we showed that those “Fitting formations” which are subgroup closed are also saturated, without restriction on nilpotent length; indeed such classes are, roughly speaking, recursively definable as local formations using a local definition consisting of such classes. It is natural to ask how these hypotheses may be weakened yet still produce the same classes of groups. Already in [10] Hawkes showed that Fitting formations need be neither subgroup closed nor saturated; and in [3] we showed that a saturated Fitting formation need not be subgroup closed (though a Fitting formation of groups of nilpotent length three is saturated if and only if it is subgroup closed).
Publisher
Cambridge University Press (CUP)
Reference16 articles.
1. Some product varieties of groups
2. Varieties of Groups
3. [4] Cossey P. J. , On varieties of A-groups, (Ph. D. Thesis, Australian National University, 1966).
4. Fitting formations of finite soluble groups
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1. A Hall-type closure property for certain Fitting classes;Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics;1995-10
2. Bibliography;Finite Soluble Groups;1992-12-31
3. The fitting class generated by a finite soluble group;Annali di Matematica Pura ed Applicata;1991-12
4. Fittingklassen mit zus�tzlichen Abschlu�eigenschaften;Archiv der Mathematik;1988-01
5. Sub-direct product closed Fitting classes;Bulletin of the Australian Mathematical Society;1986-02