Essential subgroup

From Citizendium, the Citizens' Compendium

	Main Article	Talk	Related Articles  [?]	Bibliography  [?]	External Links  [?]
	This is a draft article, under development and not meant to be cited but you can help to improve it. These unapproved articles are subject to a disclaimer. [edit intro]

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.

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

• Phillip A. Griffith (1970). Infinite Abelian group theory. University of Chicago Press. ISBN 0-226-30870-7.