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Relative normal complements and extendibility of characters. (English) Zbl 0519.20022


MSC:

20D40 Products of subgroups of abstract finite groups
20C15 Ordinary representations and characters
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
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References:

[1] R. Brauer, On quotient groups of finite groups. Math. Z.83, 72–84 (1964). · Zbl 0116.01802 · doi:10.1007/BF01111110
[2] E. C. Dade, On normal complements to sections of finite groups. J. Austral. Math. Soc.19 (Series A), 257–262 (1975). · Zbl 0319.20031 · doi:10.1017/S1446788700031451
[3] W.Feit, Characters of finite groups. New York 1967. · Zbl 0166.29002
[4] P. Ferguson, Relative normal complements in finite groups. Proc. Amer. Math. Soc.87, 38–40 (1983). · Zbl 0509.20013 · doi:10.1090/S0002-9939-1983-0677226-5
[5] D.Gorenstein, Finite groups. New York 1968. · Zbl 0185.05701
[6] I. M.Isaacs, Character theory of finite groups. New York 1976. · Zbl 0337.20005
[7] H. S. Leonard andK. K. McKelvey, On lifting characters in finite groups. J. Alg.7, 168–191 (1967). · Zbl 0189.32103 · doi:10.1016/0021-8693(67)90054-3
[8] H. S. Leonard, On relative normal complements in finite groups. Arch. Math.40, 97–108 (1983). · Zbl 0511.20015 · doi:10.1007/BF01192757
[9] C. H. Sah, Existence of normal complements and extension of characters in finite groups. Ill. J. Math.6, 282–291 (1962). · Zbl 0105.25602
[10] M. Suzuki, On the existence of a Hall normal subgroup. J. Math. Soc. Japan15, 387–391 (1963). · Zbl 0119.26702 · doi:10.2969/jmsj/01540387
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