Jacobson radical

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This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
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Definition

Symbol-free definition

The Jacobson radical (also the Baer radical) of a group is defined in the following equivalent ways:

In terms of the intersect-all operator

This property is obtained by applying the intersect-all operator to the property: maximal normal subgroup
View other properties obtained by applying the intersect-all operator

Equivalence of definitions

The equivalence of these definitions follows from Baer's theorem.