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The \(\mathfrak F\)-normalizers of a finite soluble group. (English) Zbl 0167.29201


MSC:

20F16 Solvable groups, supersolvable groups
20F17 Formations of groups, Fitting classes
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References:

[1] Alperin, J. L., Normalizers of system normalizers, Trans. Am. Math. Soc., 113, 181-188 (1964) · Zbl 0123.02502
[2] Alperin, J. L., System normalizers and Carter subgroups, J. Algebra, 1, 355-366 (1964)
[3] Carter, R. W., On a class of finite soluble groups, (Proc. London Math. Soc., 9 (1959)), 623-640, (3) · Zbl 0168.27205
[4] Carter, R. W., Splitting properties of soluble groups, J. London Math. Soc., 36, 89-94 (1961) · Zbl 0104.24903
[5] Carter, R. W., Nilpotent self-normalizing subgroups of soluble groups, Math. Z., 75, 136-139 (1961) · Zbl 0168.27301
[6] Carter, R. W., Nilpotent self-normalizing subgroups and system normalizers, (Proc. London Math. Soc., 12 (1962)), 535-563 · Zbl 0106.24602
[7] Gaschütz, W., Über die Φ-Untergruppe endlicher Gruppen, Math. Z., 58, 160-170 (1953) · Zbl 0050.02202
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[9] Gaschütz, W.; Lubeseder, U., Kennzeichnung gesättigter Formationen, Math. Z., 82, 198-199 (1963) · Zbl 0116.25603
[10] Hall, P., On the Sylow systems of a soluble group, (Proc. London Math. Soc., 43 (1937)), 316-323 · JFM 63.0069.04
[11] Hall, P., On the system normalizers of a soluble group, (Proc. London Math. Soc., 43 (1937)), 507-528 · Zbl 0018.01001
[12] Hawkes, T. O., A note on system normalizers, (Proc. Cambridge Phil. Soc., 62 (1966)), 339-346 · Zbl 0145.02902
[13] Higman, G., Complementation of Abelian normal subgroups, Publ. Math. Debrecen., 4, 455-458 (1956) · Zbl 0075.23904
[14] Huppert, B., Normalteiler und maximale Untergruppen endlicher Gruppen, Math. Z., 60, 409-434 (1954) · Zbl 0057.25303
[15] Lubeseder, U.; Lubeseder, U.
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