Geodesic
Prefrattini Subgroups and Cover-Avoidance Properties in U-Groups
Canadian journal of mathematics, Tome 27 (1975) no. 4, pp. 837-851

Voir la notice de l'article provenant de la source Cambridge University Press

W. Gaschutz [5] introduced a conjugacy class of subgroups of a finite soluble group called the prefrattini subgroups. These subgroups have the property that they avoid the complemented chief factors of G and cover the rest. Subsequently, these results were generalized by Hawkes [12], Makan [14; 15] and Chambers [2]. Hawkes [12] and Makan [14] obtained conjugacy classes of subgroups which avoid certain complemented chief factors associated with a saturated formation or a Fischer class. Makan [15] and Chambers [2] showed that if W, D and V are the prefrattini subgroup, J-normalizer and a strongly pronormal subgroup associated with a Sylow basis S, then any two of W, D and V permute and the products and intersections of these subgroups have an explicit cover-avoidance property. 
Tomkinson, M. J. Prefrattini Subgroups and Cover-Avoidance Properties in U-Groups. Canadian journal of mathematics, Tome 27 (1975) no. 4, pp. 837-851. doi: 10.4153/CJM-1975-091-1
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[1] 1. Birkhoff, G., Lattice theory, Second Ed. (Amer. Math. Soc, Providence, R.I., 1964). Google Scholar

[2] 2. Chambers, G. A., On f-Prefrattini subgroups, Can. Math. Bull. 15 (1972), 345–348. Google Scholar

[3] 3. Gardiner, A. D., Hartley, B., and Tomkinson, M. J., Saturated formations and Sylow structure in locally finite groups, J. Algebra 17 (1971), 177–211. Google Scholar

[4] 4. Gaschutz, W., Uber die S-Untergruppe endlicher Gruppen, Math. Z. 56 (1952), 376–387. Google Scholar

[5] 5. Gaschutz, W., Praefrattinigruppen, Arch. Math. 13 (1962), 418–426. Google Scholar

[6] 6. Graddon, C. J., Some generalizations, to certain locally finite groups, of theorems due to Chambers and Rose, Illinois J. Math. 17 (1973), 666–679. Google Scholar

[7] 7. Hartley, B., C-abnormal subgroups of certain locally finite groups, Proc. London Math. Soc. 23 (1971), 228–258. Google Scholar

[8] 8. Hartley, B., Sylow theory in locally finite groups, Compositio Math. 25 (1972), 263–280. Google Scholar

[9] 9. Hartley, B., Some examples of locally finite groups, Arch. Math. 23 (1972), 225–231. Google Scholar

[10] 10. Hartley, B., A class of modules over a locally finite group, I. J. Austral. Math. Soc. 16 (1973), 431–442. H# Aclass 0f modules over a locally finite group III, to appear. Google Scholar

[12] 12. Hawkes, T. o., Analogues of Prefrattini subgroups, Proc. Internat. Conf. Theory of Groups, Austral. Nat. Univ. Canberra, August 1965, pp. 145–150 (Gordon and Breach, New York, 1967). Google Scholar

[13] 13. A note on system normalizers of a finite soluble group, Proc. Cambridge Philos. Soc. 62 (1966), 339–346. Google Scholar

[14] 14. Makan, A. R., Another characteristic conjugacy class of subgroups of finite soluble groups, J. Austral. Math. Soc. 11 (1970), 395–400. Google Scholar

[15] 15. Makan, A. R., On certain sublattices of the lattice of subgroups generated by the Prefrattini subgroups, the injectors and the formation subgroups, Can. J. Math. 25 (1973), 862–869. Google Scholar

[16] 16. Tomkinson, M. J., Formations of locally soluble FC-groups, Proc. London Math. Soc. 19 (1969), 675–708. Google Scholar

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