Exercise · ZW-INDEX-OF-A-SUBGROUP-009 · ★★★ Advanced
If \([G:H]=2\), what are the left cosets of \(H\)?
Choose one option.
Show answer
- B. \(H\) and its complement \(G\setminus H\)
Explanation
There are exactly two cosets, they are disjoint, and their union is \(G\). One is \(H\), so the other must be everything left over, \(G\setminus H\).
Review the concept: Index of a subgroup
The index of a subgroup \(H\) of a group \(G\) is the number of distinct left cosets of \(H\) in \(G\).
\[[G:H]\]
More practice problems: index of a subgroup
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