Subdirectly irreducible 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 standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definition
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Definition

Symbol-free definition

A group is said to be subdirectly irreducible if:

  • Any expression of the group as subdirect product has that the projection map to at least one of the factors is an isomorphism
  • The trivial subgroup of the group cannot be expressed as an intersection of two nontrivial normal subgroups

Relation with other properties

Stronger properties

Weaker properties