6533b853fe1ef96bd12ac1d9
RESEARCH PRODUCT
Group Extensions and Graphs
Ramon Esteban-romeroEnric Cosme LlópezAdolfo Ballester-bolinchessubject
Information retrievalOperations researchNoticebusiness.industryGeneral Mathematics010102 general mathematicsGrups Teoria de01 natural sciencesGraphGraph010101 applied mathematicsDisk formattingMathematics::Group TheoryPublishingGroup0101 mathematicsbusinessMATEMATICA APLICADAGroup extensionMatemàticaMathematicsdescription
A classical result of Gaschütz affirms that given a finite A-generated group G and a prime p, there exists a group G# and an epimorphism phi: G# ---> G whose kernel is an elementary abelian p-group which is universal among all groups satisfying this property. This Gaschütz universal extension has also been described in the mathematical literature with the help of the Cayley graph. We give an elementary and self-contained proof of the fact that this description corresponds to the Gaschütz universal extension. Our proof depends on another elementary proof of the Nielsen-Schreier theorem, which states that a subgroup of a free group is free.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 |