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Finite groups admitting a fixed-point-free 2-automorphism. (English) Zbl 0403.20015

MSC:

20D15 Finite nilpotent groups, \(p\)-groups
20D45 Automorphisms of abstract finite groups
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References:

[1] F. Gross, ”Groups admitting a fixed-point-free automorphism of order 2n,” Pac. J. Math.,24, No. 2, 269–275 (1968). · Zbl 0157.05702
[2] J. G. Thompson, ”Finite groups with fixed-point-free automorphisms of prime order,” Proc. Nat. Acad. Sci.,45, 578–581 (1959). · Zbl 0086.25101 · doi:10.1073/pnas.45.4.578
[3] J. G. Thompson, ”Automorphisms of solvable groups,” J. Algebra,1, 259–267 (1964). · Zbl 0123.02602 · doi:10.1016/0021-8693(64)90022-5
[4] E. Shult, ”On groups admitting fixed-point-free Abelian groups,” Illinois J. Math.,9, No. 4, 701–720 (1965). · Zbl 0136.28504
[5] F. Hoffman, ”Nilpotent height of finite groups admitting fixed-point-free automorphisms,” Math. Z.,85, 260–267 (1964). · Zbl 0126.27001 · doi:10.1007/BF01112147
[6] F. Gross, ”Solvable groups admitting a fixed-point-free automorphism of prime power order,” Proc. Am. Math. Soc.,17, 1440–1446 (1966). · Zbl 0147.27201 · doi:10.1090/S0002-9939-1966-0207836-0
[7] B. Scimemi, ”Un’osservazione sui gruppi finiti dotati di automorfismi di ordine pn privi di coincidenze,” Atti Accad. Naz. Lincei Rend.,54, No. 4, 509–510 (1973). · Zbl 0284.20027
[8] C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience, New York-London (1962).
[9] D. Gorenstein, Finite Groups, Harper and Row, New York-Evanston-London (1968).
[10] J. G. Thompson, ”A special class of nonsolvable groups,” Math. Z.,72, No. 5, 458–462 (1960). · Zbl 0093.02601 · doi:10.1007/BF01162968
[11] F. Gross, ”Elementary Abelian operator groups,” Bull. Austral. Math. Soc.,7, No. 1, 91–101 (1972). · Zbl 0241.20016 · doi:10.1017/S0004972700044841
[12] V. M. Busarkin and Yu. M. Gorchakov, Finite Groups That Admit Partitions [in Russian], Nauka, Moscow (1968).
[13] T. R. Berger, ”Solvable groups, automorphism groups, and representation theory,” in: T. Gagen, M. P. Hale, Jr., and E. E. Shult (editors), Finite Groups ’72, Proc. Gainesville Conference on Finite Groups, March 23–24, 1972, North-Holland, Amsterdam-London (1973), pp. 19–24.
[14] T. R. Berger, ”Nilpotent fixed-point-free automorphism groups of solvable groups,” Math. Z.,131, No. 4, 305–312 (1973). · Zbl 0257.20018 · doi:10.1007/BF01174905
[15] T. R. Berger, ”Automorphisms of solvable groups,” J. Algebra,27, No. 2, 311–340 (1973). · Zbl 0281.20010 · doi:10.1016/0021-8693(73)90108-7
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