On maximal and Sylow subgroups of finite solvable groups.
Let \(G\) be a finite group. \(G\) is said to be bicyclic if it is the product of two cyclic subgroups. The structure of a finite solvable group with bicyclic Sylow subgroups is studied. In particular, it is proved that the nilpotent length of these groups is not greater than 4. Since in any finite solvable group the index of each maximal subgroup is a prime power the structure of a finite solvable group with the index of each maximal subgroup either a prime or the square of a prime or the cube of a prime is studied also. It is proved that the supersolvable coradical of \(G\) is an extension of a metanilpotent group by a 2-group and the nilpotent length of such a group does not exceed 5.
scientific article; zbMATH DE number 1927787