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On a relation between the Fitting length of a soluble group and the number of conjugacy classes of its maximal nilpotent subgroups

Published online by Cambridge University Press:  17 April 2009

H. Lausch  and
A. Makan
H. Lausch
Affiliation:
Department of Mathematics, IAS, The Australian National University, Canberra, A.C.T.
A. Makan
Affiliation:
Department of Mathematics, IAS, The Australian National University, Canberra, A.C.T.
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Abstract

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In a finite soluble group G, the Fitting (or nilpotency) length h(G) can be considered as a measure for how strongly G deviates from being nilpotent. As another measure for this, the number v(G) of conjugacy classes of the maximal nilpotent subgroups of G may be taken. It is shown that there exists an integer-valued function f on the set of positive integers such that h(G) ≦ f(v(G)) for all finite (soluble) groups of odd order. Moreover, if all prime divisors of the order of G are greater than v(G)(v(G) - l)/2, then h(G) ≦3. The bound f(v(G)) is just of qualitative nature and by far not best possible. For v(G) = 2, h(G) = 3, some statements are made about the structure of G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 1 , April 1969 , pp. 3 - 10
Copyright
Copyright © Australian Mathematical Society 1969

References

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