6533b822fe1ef96bd127cd01

RESEARCH PRODUCT

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

A. Martínez-pastorLev KazarinMaría Dolores Pérez-ramos

subject

Normal subgroupFinite groupAlgebra and Number TheoryGroup (mathematics)Products of groupsHall subgroupsCombinatoricsSet (abstract data type)π-Decomposable groupsProduct (mathematics)MATEMATICA APLICADAπ-GroupsMathematics

description

[EN] The main result in the paper states the following: Let π be a set of odd primes. Let the finite group G=AB be the product of a π -decomposable subgroup A=Oπ(A)×Oπ′(A) and a π -subgroup B . Then Oπ(A)⩽Oπ(G); equivalently the group G possesses Hall π -subgroups. In this case Oπ(A)B is a Hall π-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.

yearjournalcountryeditionlanguage
2007-09-01Journal of Algebra
https://doi.org/10.1016/j.jalgebra.2007.06.004