Exercise · ZW-INDEX-OF-A-SUBGROUP-005 · ★☆☆ Basic
Which subgroup \(H\) of a group \(G\) has index \(1\)?
Choose one option.
Show answer
- C. \(G\) itself, since there is only one coset
Explanation
If \([G:H]=1\) there is a single coset, and since \(H\) is one of them, \(H=G\). The trivial subgroup has index \(|G|\).
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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