6533b822fe1ef96bd127ce68
RESEARCH PRODUCT
Existence of normal Hall subgroups by means of orders of products
Azahara SáezAntonio Beltránsubject
010101 applied mathematicsPure mathematicsp-nilpotent groupsGeneral Mathematics010102 general mathematicsproduct of elements0101 mathematics01 natural sciencesHall subgroupsMathematicsorder of elementsdescription
Let G be a finite group, let π be a set of primes and let p be a prime. We characterize the existence of a normal Hall π‐subgroup in G in terms of the order of products of certain elements of G. This theorem generalizes a characterization of A. Moretó and the second author by using the orders of products of elements for those groups having a normal Sylow p‐subgroup 6. As a consequence, we also give a π‐decomposability criterion for a finite group also by means of the orders of products.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-11-12 |