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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.

##### MSC:
 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