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On Certain Sublattices of the Lattice of Subgroups Generated by the Prefrattini Subgroups, the Injectors and the Formation Subgroups

Published online by Cambridge University Press:  20 November 2018

A. R. Makan
A. R. Makan*
Affiliation:
University of Alberta, Edmonton, Alberta; University of Kentucky, Lexington, Kentucky
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Various characteristic conjugacy classes of subgroups having covering/avoidance properties with respect to chief factors have recently played a major role in the study of finite soluble groups. Apart from the subgroups which are now called Hall subgroups, P. Hall [7] also considered the system normalizers of a finite soluble group and showed that these form a characteristic conjugacy class, cover the central chief factors and avoid the rest. The system normalizers were later shown by Carter and Hawkes [1] to be the simplest example of a wealth of characteristic conjugacy classes of subgroups of finite soluble groups which arise naturally as a consequence of the theory of formations.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 862 - 869
Copyright
Copyright © Canadian Mathematical Society 1973

References

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