Core-free 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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This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
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View a list of other standard non-basic definitions


Symbol-free definition

A finite group is said to be core-free if it satisfies the following conditions:

  • It has no nontrivial normal subgroup of odd order
  • The Brauer core is trivial

Relation with other properties

Stronger properties