Definition:Congruence Modulo Subgroup/Left Congruence/Also known as
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Definition
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
Let $\RR^l_H$ be the relation of left congruence modulo $H$ (in $G$).
When $\tuple {x, y} \in \RR^l_H$, we write:
- $x \equiv^l y \pmod H$
which is read: $x$ is left congruent to $y$ modulo $H$.
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 42$. Another approach to cosets