Onto extensions of free groups

Groups Complexity Cryptology

article

Sebastià Mijares¹  Enric Ventura² 

[1] Departament d’Enginyeria Inform`atica i de les Comunicacions, Universitat Aut`onoma de Barcelona;Departament de Matem`atiques, Universitat Polit`ecnica de Catalunya, and Institut de Matem`atiques de la UPC-BarcelonaTech

关键词: Free group;    subgroup extension;    onto extension;    algebraic extension;    Stallingsgraph;   

DOI  :  10.46298/jgcc.2021.13.1.7036

来源: Episciences

【 摘 要 】

An extension of subgroups H 6 K 6 FA of the free group of rank |A| = r > 2is called onto when, for every ambient basis A0, the Stallings graph ΓA0 (K) is a quotient ofΓA0 (H). Algebraic extensions are onto and the converse implication was conjectured byMiasnikov–Ventura–Weil, and resolved in the negative, first by Parzanchevski–Puder forrank r = 2, and recently by Kolodner for general rank. In this note we study propertiesof this new type of extension among free groups (as well as the fully onto variant), andinvestigate their corresponding closure operators. Interestingly, the natural attempt for adual notion –into extensions– becomes trivial, making a Takahasi type theorem not possiblein this setting.

【 授权许可】

Unknown