Let \({\mathcal {D}}\) be a 2-\((v,k,\lambda )\) symmetric design with k and \(\lambda \) prime powers. If \({\mathcal {D}}\) admits a flag-transitive, point-imprimitive automorphism group G, we show that both k and \(\lambda \) must be powers of 2. Moreover, there exists an integer m such that either (a) \({\mathcal {D}}\) has parameters \((v,k,\lambda )=(2^{2m+2}-1, 2^{2m+1}, 2^{2m})\), and G preserves a partition of the points into \(2^{m+1}+1\) classes of size \(2^{m+1}-1\), or (b) \({\mathcal {D}}\) has parameters \((v,k,\lambda )=((2^{2m-1}-2^m+1)(2^{m-1}+1),\ 2^{2m-1},\ 2^m)\), and G preserves a partition of the points into \(2^{2m-1}-2^m+1\) classes of size \(2^{m-1}+1\).

让\（{\ mathcal {d}} \）是2- \（（V，K，\拉姆达）\）的对称设计具有ķ和\（\拉姆达\）素权力。如果\（{\ mathcal {D}} \）允许一个标志传递，点同质自同构群G，则表明k和\（\ lambda \）都必须是2的幂。此外，存在一个整数m这样（a）\ {{\ mathcal {D}} \）的参数\（（v，k，\ lambda）=（2 ^ {2m + 2} -1，2 ^ {2m + 1}，2 ^ {2m}）\），G将点的划分保留为大小为\（2 ^ {m + 1} -1 \）的\（2 ^ {m + 1} +1 \）类。或（b）\（{\ mathcal {D}} \）的参数\（（v，k，\ lambda）=（（（2 ^ {2m-1} -2 ^ m + 1）（2 ^ {m -1} +1），\ 2 ^ {2m-1}，\ 2 ^ m）\）和G将点的分区保留为\（2 ^ {2m-1} -2 ^ m + 1 \）大小为\（2 ^ {m-1} +1 \）的类。