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Another characteristic conjugacy class of subgroups of finite soluble groups

Published online by Cambridge University Press:  09 April 2009

A. Makan
A. Makan
Affiliation:
Department of MathematicsInstitute of Advanced StudiesAustralian National UniversityP.O. Box 4, CANBERRA
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Let name be a class of finite soluble groups with the properties: (1) is a Fitting class (i.e. normal subgroup closed and normal product closed) and (2) if N ≦ H ≦ G ∈, N ⊲ G and H/N is a p-group for some prime p, then H ∈. Then is called a Fischer class. In any finite soluble group G, there exists a unique conjugacy class of maximal -subgroups V called the -injectors which have the property that for every N◃◃G, N ∩ V is a maximal -subgroup of N [3]. 3. By Lemma 1 (4) [7] an -injector V of G covers or avoids a chief factor of G. As in [7] we will call a chief factor -covered or -avoided according as V covers or avoids it and -complemented if it is complemented and each of its complements contains some -injector. Furthermore we will call a chief factor partially-complemented if it is complemented and at least one of its complements contains some -injector of G.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 4 , November 1970 , pp. 395 - 400
Copyright
Copyright © Australian Mathematical Society 1970

References

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