# Changes

## Left cosets partition a group

, 21:38, 4 May 2010
Statement with symbols
# The left cosets of $H$, namely $gH, g \in G$, form a partition of the group $G$. In other words, $G$ is a disjoint union of left cosets of $H$.
# The relation $a \sim b \iff a \in bH$ is an equivalence relation on $G$
# For every $g \in G$, there is ''exactly'' one left coset of $H$ in $G$ containing $g$.
# If $aH$ and $bH$ are left cosets of $H$ in $G$, then either $aH = bH$ or $aH \cap bH$ is empty.