View source for Essential subgroup


A  [[subgroup]] that determines much of the structure of its containing  group.  The concept may be generalized to [[essential submodule]]s.

A  [[subgroup]] $S$ of a (typically [[abelian group|abelian]]) [[group]]  $G$ 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, ''Infinite Abelian group theory'', Chicago  Lectures in Mathematics (University of Chicago Press, 1970) {{ISBN|0-226-30870-7}} p.19