Schur multipliers and power endomorphisms of groups
Copyright policy )Schur multipliers and power endomorphisms of groups
A group \(G\) is said to be \(n\)-central if \(\exp(G/Z(G))\) divides \(n\). Clearly, if \(\exp(G)=n\), then a representation group of \(G\) is \(n\)-central. Using his results on \(n\)-central groups, the author proves some new estimates of \(\exp(M(G))\), where \(M(G)\) is the Schur multiplier of \(G\). As a consequence, he proves that if \(G\) is a metabelian group of exponent \(p\), then \(\exp(M(G))\) divides \(p\) (in fact, according to D. L. Johnson, we have \(\exp(M(G))=p\) here). Next, if \(\exp(G)=4\), then \(\exp(M(G))\) divides \(8\), and this is the best possible result.
powerful \(p\)-groups, Central extensions and Schur multipliers, Algebra and Number Theory, Schur multiplier, \(n\)-central groups, power endomorphisms, p-Group, Automorphisms of abstract finite groups, Quasivarieties and varieties of groups, General structure theorems for groups, finite \(p\)-groups, Finite nilpotent groups, \(p\)-groups, Derived series, central series, and generalizations for groups, Periodic groups; locally finite groups, Power endomorphism, exponents, exponential ranks, Schur multipliers
powerful \(p\)-groups, Central extensions and Schur multipliers, Algebra and Number Theory, Schur multiplier, \(n\)-central groups, power endomorphisms, p-Group, Automorphisms of abstract finite groups, Quasivarieties and varieties of groups, General structure theorems for groups, finite \(p\)-groups, Finite nilpotent groups, \(p\)-groups, Derived series, central series, and generalizations for groups, Periodic groups; locally finite groups, Power endomorphism, exponents, exponential ranks, Schur multipliers
selected citations These citations are derived from selected sources.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).20 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.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!