AI 中文总结
该研究构造了一个2生成的无扭幂零群，其幂零类为6且所有子群均为亏格至多5的次正规，从而否定了Casolo关于此类群幂零类与亏格关系的问题在n=5时的结论。
AI 中文摘要
Casolo提出问题：每个子群都是亏格至多n的次正规的无扭群是否必为类至多n的幂零群。n≤4时答案为肯定。我们构造了一个2生成的无扭幂零群G，满足幂零类cl(G)=6，且对G的每个子群H，有[G,₅H]≤H，由此得出n=5时该问题答案为否定。
英文摘要
Casolo asked whether a torsion-free group in which every subgroup is subnormal of defect at most $n$ must be nilpotent of class at most $n$. The answer is known to be positive for $n\leq 4$. We construct a $2$-generated torsion-free nilpotent group $G$ such that $$ \cl(G)=6 \qquad\text{and}\qquad [G,{}_5H]\leq H \quad\text{for every }H\leq G. $$ Thus Casolo's question has a negative answer for $n=5$.
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