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On locally graded groups. (English) Zbl 0871.20023

Kim, A. C. (ed.) et al., Groups - Korea ’94. Proceedings of the international conference, Pusan, Korea, August 18-25, 1994. Berlin: Walter de Gruyter. 189-197 (1995).
A group \(G\) is called locally graded if every finitely generated non-trivial subgroup of \(G\) has a finite non-trivial quotient. This is a wide class of groups that includes all generalized solvable groups and all residually finite groups. In this paper certain results which are known to hold for solvable or residually finite groups are extended to the class of locally graded groups. For example it is proved that if \(G\) is a locally graded \(n\)-Engel group then \(G\) is locally nilpotent.
For the entire collection see [Zbl 0857.00028].

MSC:

20E25 Local properties of groups
20E26 Residual properties and generalizations; residually finite groups
20F45 Engel conditions
20F19 Generalizations of solvable and nilpotent groups
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