6533b828fe1ef96bd1288399

RESEARCH PRODUCT

Permutable products of supersoluble groups

Manuel J. AlejandreJohn CosseyAdolfo Ballester-bolinches

subject

CombinatoricsNilpotentAlgebra and Number TheoryIntersectionGroup (mathematics)Product (mathematics)Structure (category theory)Permutable primeQuotient groupMathematics

description

We investigate the structure of finite groups that are the mutually permutable product of two supersoluble groups. We show that the supersoluble residual is nilpotent and the Fitting quotient group is metabelian. These results are consequences of our main theorem, which states that such a product is supersoluble when the intersection of the two factors is core-free in the group.

yearjournalcountryeditionlanguage
2004-06-01Journal of Algebra
https://doi.org/10.1016/j.jalgebra.2003.01.002