- 試証: 若 G 有一合成級數，則任何正規子群 G 都有合成級數。
- 試証: 若 N 在 G 中為正規，且若 G 有一合成級數，則 G/N 亦然。
- Suppose that G has a composition series and that N is normal in G . Prove that G has a composition series of which N is a member.
- Suppose that G has a composition series. Prove that any normal
series of G has a refinement that is a composition series.
- (<#68#>Zassenhaus's Lemma<#68#>) Let <#69#>A<#69#> and B
be subgroups of a group G, and let M and N be normal in <#70#>A<#70#> and
B, respectively. Prove that