Group of finite homological type

From Groupprops
Jump to: navigation, search
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of finiteness (groups)|Find other variations of finiteness (groups) |

This property makes sense for infinite groups. For finite groups, it is always true

Definition

Symbol-free definition

A group is said to be of finite homological type if it has subgroups of finite index which have finite cohomological dimension, and if every such subgroup has finitely generated integral homology. For such groups we can define an Euler characteristic and perform many other homological constructions.

References

  • Euler characteristics of discrete groups and G-spaces by Kenneth S. Brown
  • Euler characteristics of groups by Kenneth S. Brown