Locally graded groups with a nilpotency condition on infinite subsets (Q2707067)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Locally graded groups with a nilpotency condition on infinite subsets |
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Locally graded groups with a nilpotency condition on infinite subsets (English)
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9 January 2002
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locally graded groups
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nilpotent groups
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finitely generated subgroups
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finite quotient groups
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central series
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A group is called locally graded if each non-trivial finitely generated subgroup has a non-trivial finite quotient. Here the authors study locally graded groups in the class \(N(2,k)^*\): this is the class of groups in which every infinite subset contains a pair of elements generating a nilpotent subgroup of class at most \(k\).NEWLINENEWLINENEWLINEThe main result of the paper is: Theorem 1. Let \(G\) be a finitely generated, locally graded group in the class \(N(2,k)^*\). Then \(G/Z_c(G)\) is finite for some \(c=c(k)>0\).
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