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Abstract Algebra

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Moderate

Cosets of a Subset

ABSALG-LK5LSE

Let $G$ be a finite group and $H$ be a subset of $G$. Identify which of the following statements are true.

A

The set of right cosets of $H$ forms a partition of $G$.

B

$|aH|=|bH|$ for $a,b \in G$.

C

$|H|$ divides $|G|$.

D

The set of left cosets and right cosets of $H$ in $G$ are equal.