On Torsion-by-Nilpotent Groups
Copyright policy )On Torsion-by-Nilpotent Groups
Here are the main results of the article under review: Theorem 1.1. Let \(\wp\) be a class of groups, which is closed under taking subgroups and quotients. Suppose that all metabelian groups of \(\wp\) are torsion-by-nilpotent. Then all soluble groups of \(\wp\) are torsion-by-nilpotent. Theorem 1.2. Let \(H\) be a normal subgroup of a group \(G\). If \(G/H'\) and \(H\) are (locally finite)-by-nilpotent, then \(G\) is (locally finite)-by-nilpotent. The last result is a generalization of Hall's well-known theorem on the nilpotency of a group \(G\), in which a normal subgroup \(H\) and the quotient \(G/H'\) are nilpotent.
General structure theorems for groups, Algebra and Number Theory, (locally finite)-by-nilpotent groups, soluble groups, Generalizations of solvable and nilpotent groups, torsion-by-nilpotent groups, metabelian groups, nilpotency
General structure theorems for groups, Algebra and Number Theory, (locally finite)-by-nilpotent groups, soluble groups, Generalizations of solvable and nilpotent groups, torsion-by-nilpotent groups, metabelian groups, nilpotency
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!