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On f-Prefrattini Subgroups

Published online by Cambridge University Press:  20 November 2018

Graham A. Chambers
Graham A. Chambers*
Affiliation:
University of Alberta, Edmonton, Alberta
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The Prefrattini subgroups of a finite soluble group were introduced by Gaschutz [3]. These are a conjugacy class of subgroups which avoid complemented chief factors and cover Frattini chief factors. Gaschutz [3, Satz 7.1] showed that if G has p-length 1 for each prime p, and if U≤G avoids all complemented chief factors and covers all Frattini factors, then U is a Prefrattini subgroup of G. We begin by proving the analogous result for the f-Prefrattini subgroups introduced by Hawkes [5], If f is a saturated formation, then the f-Prefrattini subgroups of G are a conjugacy class of subgroups which avoid f-eccentric complemented chief factors of G and cover all other chief factors of G.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 3 , September 1972 , pp. 345 - 348
Copyright
Copyright © Canadian Mathematical Society 1972

References

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