Essential subgroup explained
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
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
- Book: Phillip A. Griffith . Infinite Abelian group theory . Chicago Lectures in Mathematics . . 1970 . 0-226-30870-7 . 19.
