Essential subgroup

From formulasearchengine
Jump to navigation Jump to search

In mathematics, especially in the area of algebra studying the theory of abelian groups, an essential subgroup is a subgroup that determines much of the structure of its containing group. The concept was generalized to essential submodules.

Definition

A subgroup of a (typically abelian) group is said to be essential if whenever H is a non-trivial subgroup of G, the intersection of S and H is non-trivial: here "non-trivial" means "containing an element other than the identity".

References

  • {{#invoke:citation/CS1|citation

|CitationClass=book }}


Template:Abstract-algebra-stub