MATHEMATICS

Product of two solvable subgroups of 3' index

V. N. Tyutyanov

Gomel Branch of International University, Gomel

Abstract: The restrictions on the indices of subgroups play an important role in the study of finite groups. This theme was considered by R. Guralnik, L.S. Kazarin, V.S. Monahov and other authors. Some authors investigated restrictions on the indices in the consideration of the factorization. L.S. Kazarin proved the solubility of a finite group which is the product of two soluble subgroups of odd index. V.S. Monahov studied the structure of a finite group which is factorized by the factors of prime index. He also studied the structure of a finite group which is factorized by soluble factors of odd index with a number of additional restrictions and without using the theorem on the classification of simple non-Abelian groups.

Keywords: finite group, simple nonabelian group, Frobenius group, factorized group.

UDC: 512.542

Received: 27.03.2012