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Metanilpotent fitting classes

Published online by Cambridge University Press:  09 April 2009

R. A. Bryce  and
John Cossey
R. A. Bryce
Affiliation:
School of General Studies, Australian National University, P. O. Box 4, Canberra, A.C.T., 2600, Australia
John Cossey
Affiliation:
School of General Studies, Australian National University, P. O. Box 4, Canberra, A.C.T., 2600, Australia
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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).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 3 , May 1974 , pp. 285 - 304
Copyright
Copyright © Australian Mathematical Society 1974

References

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