Geodesic
On f-Prefrattini Subgroups
Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 345-348

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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. 
Chambers, Graham A. On f-Prefrattini Subgroups. Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 345-348. doi: 10.4153/CMB-1972-062-5
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     title = {On {f-Prefrattini} {Subgroups}},
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     year = {1972},
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     number = {3},
     doi = {10.4153/CMB-1972-062-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-062-5/}
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