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Nilpotent groups admitting an almost regular automorphism of order \(4\). (English. Russian original) Zbl 0936.20032
Algebra Logika 35, No. 3, 314-333 (1996); translation in Algebra Logic 35, No. 3, 176-187 (1996).
Let \(G\) be a locally nilpotent group and let \(\varphi\) be an automorphism of \(G\) such that \(|\varphi|\) is prime and \(\varphi\) is regular (i.e., \(C_G(\varphi)=1\)). It is well known that \(G\) is nilpotent of class bounded by a function of \(|\varphi|\). In the article under review, a similar result is obtained in case \(|C_G(\varphi)|\) and \(|\varphi|\) are equal to 4.

20F18 Nilpotent groups
20E36 Automorphisms of infinite groups
20E25 Local properties of groups
20F19 Generalizations of solvable and nilpotent groups
20F50 Periodic groups; locally finite groups