We study finite groups with given indices of 2-maximal subgroups. Suppose that every 2-maximal subgroup H of a group G has the property: if H <= U <= V <= G, then vertical bar V : U vertical bar divides the square of a prime. Then G is solvable.
展开▼
机译：我们研究具有给定2个最大子群索引的有限群。假设组G的每个2个最大子组H具有以下属性：如果H <= U <= V <= G，则竖线V：U竖线将素数的平方除。那么G是可解的。
展开▼
