Max-core

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]


BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

Definition

Symbol-free definition

A subgroup of a group is termed a max-core if it satisfies the following equivalent conditions:

Definition with symbols

A subgroup N of a group G is termed a max-core if it satisfies the following equivalent conditions:

  • There is a maximal subgroup M of G such that N is the normal core of M
  • There is a primitive group action \alpha of <amth>G</math> such that the kernel of \alpha is N

Relation with other properties

Stronger properties

  • Maximal normal subgroup when the group involved has the property that every subgroup is contained in a maximal subgroup

Weaker properties

  • Subgroup containing the Frattini subgroup

Related group properties

A group is primitive if and only if the trivial subgroup is a max-core.