Balanced 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


Symbol-free definition

A finite group is said to be balanced if the Brauer core of the centralizer of any involution is contained in the Brauer core of the whole group.

Definition with symbols

A finite group G is said to be balanced if O(C_G(t)) \le O(G) for any t \in I(G).

Relation with other properties

Stronger properties