Locally nilpotent groups with an intersection property
Copyright policy )Locally nilpotent groups with an intersection property
Let B be a subgroup of \(\zeta_ r(G)\), the rth term of the upper central series of a torsion-free group G. Suppose all abelian subgroups of G having trivial intersection with B are of finite rank. Then all subgroups of G have finite upper central height. Moreover if G is locally nilpotent then it is nilpotent and has a normal subgroup \(G_ 1\) of nilpotency class at most 2r, with \(G/G_ 1\) torsion-free of finite rank. Any free nilpotent group G of class 2r has the property that all abelian subgroups intersecting trivially with \(\zeta_ r(G)\) are of finite rank.
- University of Würzburg Germany
- University of Cambridge United Kingdom
- Corpus Christi College Canada
finite upper central height, torsion-free group, trivial intersection, abelian subgroups, Generalizations of solvable and nilpotent groups, Derived series, central series, and generalizations for groups, Nilpotent groups, upper central series, Subgroup theorems; subgroup growth, Local properties of groups, free nilpotent group
finite upper central height, torsion-free group, trivial intersection, abelian subgroups, Generalizations of solvable and nilpotent groups, Derived series, central series, and generalizations for groups, Nilpotent groups, upper central series, Subgroup theorems; subgroup growth, Local properties of groups, free nilpotent group
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