Con-Cos group

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


A Con-Cos group is a group G with a normal subgroup N satisfying the following two conditions:

  • Any two non-identity elements of N are conjugate in G.
  • Every non-identity coset of N in G is a conjugacy class in G.

Note that if G is an abelian group, we can set N to be the trivial subgroup.

Relation with other properties

Stronger properties

Related properties