Element of Group is in Unique Coset of Subgroup/Left
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Theorem
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
Let $x \in G$.
There exists a exactly one left coset of $H$ containing $x$, that is: $x H$
Proof
Follows directly from:
$\blacksquare$
Also see
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 42.5$ Another approach to cosets