non-generator

Let $G$ be a group. $g\in G$ is said to be a non-generator if whenever $X$ is a generating set for $G$ then $X\setminus \{g\}$ is also a generating set for $G$.

Title	non-generator
Canonical name	Nongenerator
Date of creation	2013-03-22 12:23:43
Last modified on	2013-03-22 12:23:43
Owner	Evandar (27)
Last modified by	Evandar (27)
Numerical id	4
Author	Evandar (27)
Entry type	Definition
Classification	msc 20E99
Synonym	nongenerator
Related topic	FrattiniSubgroup
Related topic	Generator