PS-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
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


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

Definition

Symbol-free definition

A group is said to be a PS-group if it satisfies the following equivalent conditions:

Definition with symbols

A group G is said to be a PS-group if it satisfies the following equivalent conditions:

  • For any maximal subgroup M \le G, the normal core of M is a maximal normal subgroup of G
  • Given any quotient map from G to a primitive group, the image of the map is in fact a simple group.

Relation with other properties

Stronger properties