Let k be a divisor of a finite group G and Lk(G) = {x ∈ G | xk =1}. Frobenius proved that the number |Lk(G)| is always divisible by k. The following inverse problem is considered: for a given integer n, find all groups G such that max{k-1|Lk(G)| | k ∈ Div(G)} = n, where Div(G) denotes the set of all divisors of |G|. A procedure beginning with (in a sense) minimal members and deducing the remaining ones is outlined and executed for n=8.

中文翻译：

---

通过广度对有限群进行分类

让ķ是有限群的除数G和大号ķ(G) = {X∈G|Xķ=1}。Frobenius 证明了数|大号ķ(G)| 总是能被ķ. 考虑以下逆问题：对于给定的整数n, 找到所有组G这样最大{ķ-1|大号ķ(G)| |ķ∈ Div(G)} =n, 其中 Div(G) 表示 | 的所有除数的集合G|。概述并执行以（在某种意义上）最小成员并推导出剩余成员的过程n=8。