FINITE -GROUPS WITH SMALL AUTOMORPHISM GROUP
Copyright policy )FINITE -GROUPS WITH SMALL AUTOMORPHISM GROUP
For each prime$p$we construct a family$\{G_{i}\}$of finite$p$-groups such that$|\text{Aut}(G_{i})|/|G_{i}|$tends to zero as$i$tends to infinity. This disproves a well-known conjecture that$|G|$divides$|\text{Aut}(G)|$for every nonabelian finite$p$-group$G$.
20D15, orders of groups, automorphism groups, Group Theory (math.GR), Automorphisms of abstract finite groups, finite \(p\)-groups, Finite nilpotent groups, \(p\)-groups, cohomology of groups, QA1-939, FOS: Mathematics, 20D15 (primary), Limits, profinite groups, 20D45 (secondary), pro-\(p\) groups, Mathematics - Group Theory, Mathematics, Arithmetic and combinatorial problems involving abstract finite groups
20D15, orders of groups, automorphism groups, Group Theory (math.GR), Automorphisms of abstract finite groups, finite \(p\)-groups, Finite nilpotent groups, \(p\)-groups, cohomology of groups, QA1-939, FOS: Mathematics, 20D15 (primary), Limits, profinite groups, 20D45 (secondary), pro-\(p\) groups, Mathematics - Group Theory, Mathematics, Arithmetic and combinatorial problems involving abstract finite groups
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).6 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!