Subgroups of Finite Index in a Free Product With Amalgamated Subgroup
Copyright policy )Subgroups of Finite Index in a Free Product With Amalgamated Subgroup
Let G be a free product of finitely many finite groups with amalgamated subgroup. Using coset diagrams, a recurrence relation is obtained for the number of subgroups, and of free subgroups, of each finite index in G. In the latter case, an asymptotic formula is derived. When the amalgamated subgroup is central, the relation takes a simpler form.
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Arithmetic functions; related numbers; inversion formulas, number of subgroups, Subgroup theorems; subgroup growth, free product of finite groups with amalgamated subgroup, free subgroups of finite index, coset diagrams
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Arithmetic functions; related numbers; inversion formulas, number of subgroups, Subgroup theorems; subgroup growth, free product of finite groups with amalgamated subgroup, free subgroups of finite index, coset diagrams
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).1 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!