On the product of a π-group and a π-decomposable group

JOURNAL OF ALGEBRA

卷:315

Article

Kazarin, L. S. ; Martinez-Pastor, A. ; Perez-Ramos, M. D.

关键词: products of groups;    pi-decomposable groups;    pi-groups;    Hall subgroups;   

DOI  :  10.1016/j.jalgebra.2007.06.004

来源: Elsevier

【 摘 要 】

The main result in the paper states the following: Let pi be a set of odd primes. Let the finite group G = AB be the product of a pi -decomposable subgroup A = 0, (A) x 0,,(A) and a pi-subgroup B. Then 0 pi (A) <= 0,(G) equivalently the group G possesses Hall pi-subgroups. In this case 0,(A)B is a Hall pi-subgroup of G. This result extends previous results of Berkovich (1966), Rowley (1977), Arad and Chillag (1981) and Kazarin (1980) where stronger hypotheses on the factors A and B of the group G were being considered. The results under consideration in the paper provide in particular criteria for the existence of non-trivial soluble normal subgroups for a factorized group G. (C) 2007 Elsevier Inc. All right reserved.

【 授权许可】

Free