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A solvable group admitting a regular splitting automorphism of prime order is nilpotent. (English. Russian original) Zbl 0426.20027
Algebra Logic 17, 402-406 (1979); translation from Algebra Logika 17, 611-618 (1978).

MSC:
20F16 Solvable groups, supersolvable groups
20E36 Automorphisms of infinite groups
20E07 Subgroup theorems; subgroup growth
20F18 Nilpotent groups
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References:
[1] Yu. M. Gorchakov, ”Infinite Frobenius groups,” Algebra Logika,4, No. 1, 15–29 (1965).
[2] Kourovka Notebook (Unsolved Problems of Group Theory) [in Russian], 5th edition, Novosibirsk (1976).
[3] O. H. Kegel, ”Die Nilpotenz der Hp-Gruppen,” Math. Z.,75, No. 4, 373–376 (1961). · Zbl 0104.24904 · doi:10.1007/BF01211033
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[9] P. Hall, ”On the finiteness of certain soluble groups,” Proc. London Math. Soc.,9, 595–622 (1959). · Zbl 0091.02501 · doi:10.1112/plms/s3-9.4.595
[10] P. J. Higgins, ”Lie rings satisfying the Engel condition,” Proc. Cambridge Phil. Soc.,50, No. 1, 8–15 (1954). · Zbl 0055.02601 · doi:10.1017/S0305004100029017
[11] G. Baumslag, ”Some aspects of groups with unique roots,” Acta Math.,104, Nos. 3–4, 217–303 (1960). · Zbl 0178.34901 · doi:10.1007/BF02546390
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