6533b7d2fe1ef96bd125df01
RESEARCH PRODUCT
Products of groups and group classes
Andrew FransmanBernhard Ambergsubject
AlgebraCombinatoricsNormal subgroupNilpotentFinite groupGroup (mathematics)General MathematicsProduct (mathematics)Cyclic groupGroup theoryPrime (order theory)Mathematicsdescription
Letχ be a Schunck class, and let the finite groupG=AB=BC=AC be the product of two nilpotent subgroupsA andB andχ-subgroupC. If for every common prime divisorp of the orders ofA andB the cyclic group of orderp is anχ-group, thenG is anχ-group. This generalizes earlier results of O. Kegel and F. Peterson. Some related results for groups of the formG=AB=AK=BK, whereK is a nilpotent normal subgroup ofG andA andB areχ-groups for some saturated formationχ, are also proved.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1994-02-01 | Israel Journal of Mathematics |