References
Bauman, S.F.: The Klein group as an automorphism group without fixed points. Pacific J. Math.18, 9–13 (1966).
Berger, T.R.: Class twop groups as fixed point free automorphism groups. Illinois J. Math.14, 121–149 (1970).
Berger, T.R.: Class twop groups as fixed point free automorphism groups. Dissertation, Calif. Inst. of Tech. 1967.
Berger, T.R.: Automorphisms of Solvable Groups. J. Algebra, to appear.
Berger, T.R.: Hall-Higman Type Theorems I. Canadian J. Math. to appear.
Berger, T.R.: Hall-Higman Type Theorems II. In manuscript.
Berger, T.R.: Hall-Higman Type Theorems III. In manuscript.
Berger, T.R.: Hall-Higman Type Theorems IV. Proc. Amer. Math. Soc. to appear.
Berger, T.R.: Nilpotent groups as fixed point free automorphism groups. Amer. Math. Soc. Notices Abstract (663-45) 99.
Berger, T.R.: Oddp groups as fixed point free automorphism groups. Illinois J. Math.15, 28–36 (1971).
Burnside, W.: Theory of Groups. 2nd edition. New York: Dover 1955.
Camina, A., Collins, M.J.: Finite groups admitting automorphisms with prescribed fixed points. In manuscript.
Collins, M.J.: Finite groups admitting almost fixed point free automorphisms. Representation Theory of Finite Groups and Related Topics, pp. 25–27. Proc. Sympos. Pure Math xxi, Providence: Amer. Math. Soc. 1971.
Dade, E.C.: Carter subgroups and Fitting heights of finite solvable groups. Illinois J. Math.13, 449–514 (1969).
Feit, W., Thompson, J.: Solvability of groups of odd order. Pacific. J. Math.13, 775–1029 (1963).
Goldschmidt, D.M.: Solvable signalizer functors on finite groups. J. Algebra21, 137–148.
Gorenstein, D., Herstein, I.N.: Finite groups admitting a fixed point free automorphism of order 4. Amer. J. Math.83, 71–78 (1961).
Gross, F.: A note on fixed point free solvable operator groups. Proc. Amer. Math. Soc.19, 1363–1365 (1968).
Gross, F.: Fixed point free operator groups of order 8. Pacific J. Math.28, 357–361 (1969).
Gross, F.: Groups admitting a fixed point free automorphism of order 2n. Pacific. J. Math.24, 269–275 (1968).
Gross, F.: Solvable groups admitting a fixed point free automorphism of prime power order. Proc. Amer. Math. Soc.17, 1440–1446 (1966).
Gross, F.: Some remarks on groups admitting a fixed point free automorphism. Canadian J. Math.20, 300–307 (1968).
Hall, P., Higman, G.: On thep length ofp solvable groups and reduction theorems for Burnside's problem. Proc. London Math. Soc. (3)6, 1–42 (1956).
Higman, G.: Groups and rings having automorphisms without nontrivial fixed elements. J. London Math. Soc.32, 321–334 (1958).
Hoffman, F.: Nilpotent height of finite groups admitting fixed point free automorphisms. Math. Z.85, 260–267 (1964).
Kurzweil, H.: Auflösbare Gruppen, die eine abelsche Automorphismengruppe gestatten, deren Fixpunktgruppe nilpotent ist. J. Algebra10, 92–101 (1968).
Kurzweil, H.: Endliche Gruppen mit Automorphismus, dessen Fixpunktgruppe eine Sylowturmgruppe ist. J. Algebra12, 216–226 (1969).
Kurzweil, H.: Eine Verallgemeinerung von fixpunktfreien Automorphismen endlicher Gruppen. Arch. Math.22, 136–145 (1971).
Kurzweil, H.:p-Automorphismen von auflösbarenp′-Gruppen. Math. Z.120, 326–354 (1971).
Martineau, R.P.: Elementary abelian fixed point free automorphism groups. Quart. J. Math. Oxford II. Ser.23, 205–212 (1972).
Martineau, R.P.: Solvability of groups admitting a fixed point free automorphism group of type (p, p). Math. Z.124, 67–72 (1972).
Ralston, E.: Solvability of finite groups admitting fixed point free automorphisms of orderrs. J. Algebra23, 164–180 (1972).
Shamash, J., Shult, E.: On groups with cyclic Carter subgroups. J. Algebra11, 564–597 (1969).
Shult, E.: Nilpotence of the commutator subgroup in groups admitting fixed point free operator groups. Pacific J. Math.17, 323–347 (1966).
Shult, E.: On groups admitting fixed point free abelian operator groups. Illinois J. Math.9, 701–720 (1965).
Thompson, J.: Automorphisms of solvable groups. J. Algebra1, 259–267 (1964).
Thompson, J.: Finite groups with fixed point free automorphisms of prime order. Proc. Nat. Acad. Sci.45, 578–581 (1959).
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Research partially supported by the National Science Foundation.
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Berger, T.R. Nilpotent fixed point free automorphism groups of solvable groups. Math Z 131, 305–312 (1973). https://doi.org/10.1007/BF01174905
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DOI: https://doi.org/10.1007/BF01174905