| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Groups |
| Type | Subgroups and cosets |
| Difficulty | Challenging +1.2 This is a group theory question requiring knowledge of basic group properties, Lagrange's theorem, and small group classification. While it tests abstract algebra concepts beyond standard A-level, the questions are mostly recall-based about small groups (orders 3-7) with minimal proof or novel reasoning required. The constraint to small orders makes it more accessible than typical FP3 abstract algebra. |
| Spec | 8.03f Subgroups: definition and tests for proper subgroups8.03g Cyclic groups: meaning of the term8.03l Isomorphism: determine using informal methods |
In this question $G$ is a group of order $n$, where $3 \leqslant n < 8$.
\begin{enumerate}[label=(\roman*)]
\item In each case, write down the smallest possible value of $n$:
\begin{enumerate}[label=(\alph*)]
\item if $G$ is cyclic, [1]
\item if $G$ has a proper subgroup of order 3, [1]
\item if $G$ has at least two elements of order 2. [1]
\end{enumerate}
\item Another group has the same order as $G$, but is not isomorphic to $G$. Write down the possible value(s) of $n$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR FP3 Q1 [5]}}