Balanced group

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

Definition

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

• Even-order solvable group