Length of Subgroup Plus Length of Quotient Group

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $G$ be a finite group.

Let $H$ be a normal subgroup of $G$.


Then:

$\map l G = \map l H + \map l {G / H}$

where:

$\map l G$ denotes the length of $G$
$G / H$ denotes the quotient group of $G$ by $H$.


Proof


Sources