Balanced group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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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