Nilpotent groups related to an automorphism. (English) Zbl 1448.20031
Summary: The aim of this paper is to state some results on an \(\alpha\)-nilpotent group, which was recently introduced by R. Barzegar and A. Erfanian [Casp. J. Math. Sci. 4, No. 2, 271–283 (2015; Zbl 1424.20038)], for any fixed automorphism \(\alpha\) of a group \(G\). We define an identity nilpotent group and classify all finitely generated identity nilpotent groups. Moreover, we prove a theorem on a generalization of the converse of the known Schur’s theorem. In the last section of the paper, we study absolute normal subgroups of a finite group.
MSC:
| 20F18 | Nilpotent groups |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20F12 | Commutator calculus |
| 20D45 | Automorphisms of abstract finite groups |
| 20E36 | Automorphisms of infinite groups |
Citations:
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