Document Zbl 0413.20015

Fitting height of solvable groups admitting fixed-point-free automorphism groups. (English) Zbl 0413.20015

J. Algebra 53, 268-295 (1978).

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MSC:

20D10	Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D45	Automorphisms of abstract finite groups

Keywords:

finite soluble groups; Fitting height; Hall-Higman methods; Frobenius group; fixed point free automorphism groups

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Full Text: DOI

References:

[1]	Berger, T. R., Class two \(p\) groups as fixed point free automorphism groups, Illinois J. Math., 14, 121-149 (1970) · Zbl 0205.03303
[2]	Berger, T. R., Nilpotent fixed point free automorphism groups of solvable groups, Math. Z., 131, 305-312 (1973) · Zbl 0246.20017
[3]	Curtis, C. W.; Reiner, I., Representation Theory of Finite Groups and Associative Algebras (1966), Interscience: Interscience New York
[4]	Dornhoff, L., Group Representation Theory, Part A (1971), Dekker: Dekker New York · Zbl 0227.20002
[5]	Feit, W., Characters of Finite Groups (1967), Benjamin: Benjamin New York · Zbl 0166.29002
[6]	Glauberman, G., Correspondences of characters for relatively prime operator groups, Canad. J. Math., 20, 1465-1488 (1968) · Zbl 0167.02602
[7]	Gorenstein, D., Finite Groups (1968), Harper & Row: Harper & Row New York · Zbl 0185.05701
[8]	Griess, R., Automorphisms of extra special groups and nonvanishing degree 2 cohomology, Pacific J. Math., 48, 403-422 (1973) · Zbl 0283.20028
[9]	Jacobson, N., Lectures in Abstract Algebra II (1953), Van Nostrand: Van Nostrand Princeton, N.J. · Zbl 0053.21204
[10]	Kaplansky, I., Fields and Rings (1969), Univ. of Chicago Press: Univ. of Chicago Press Chicago
[11]	Shult, E., Nilpotence of the commutator subgroup in groups admitting fixed point free operator groups, Pacific J. Math., 17, 323-347 (1966) · Zbl 0136.28601
[12]	Shult, E., On groups admitting fixed point free Abelian operator groups, Illinois J. Math., 9, 701-720 (1965) · Zbl 0136.28504
[13]	Thompson, J., Finite groups with fixed point free automorphisms of prime order, (Proc. Nat. Acad. Sci. U.S.A., 45 (1959)), 578-581 · Zbl 0086.25101

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