essential subgroup

A subgroup $H$ of a group $G$ is essential if $H\cap K\ne \left\{e\right\}$ for any subgroup $K$ of $G$, $K\ne \left\{e\right\}$ (i.e., a subgroup $H$ of $G$ is called essential if it intersects non-trivially every non-trivial subgroup of $G$).

Title	essential subgroup
Canonical name	EssentialSubgroup
Date of creation	2013-03-22 15:31:05
Last modified on	2013-03-22 15:31:05
Owner	gh0st (10693)
Last modified by	gh0st (10693)
Numerical id	5
Author	gh0st (10693)
Entry type	Definition
Classification	msc 20F99
Related topic	Group
Related topic	Subgroup
Related topic	EssentialSubmodule