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- W2605784693 abstract "In the first part of this thesis, we study the structure of approximate subgroups inside metabelian groups (solvable groups of derived length 2) and show that if A is such a K-approximate subgroup, then it is K^(O(r)) controlled (in the sense of Tao) by a nilpotent group where r denotes the rank of G=Fit(G) and Fit(G) is the fitting subgroup of G.The second part is devoted to the study of growth of sets inside GLn(Fq) , where we show a bound on the diameter (with respect to any set of generators) for all finite simple subgroups of this group. What we have is - if G is a finite simple group of Lie type with rank n, and its base field has bounded size, then the diameter of the Cayley graph C(G; S) would be bounded by exp(O(n(logn)^3)). If the size of the base field Fq is not bounded then our method gives a bound of q^(O(n(log nq)3)) for the diameter.In the third part we are interested in the growth of sets inside commutative Moufang loops which are commutative loops respecting the moufang identities but without (necessarily)being associative. For them we show that if the sizes of the associator sets are bounded then the growth of approximate substructures inside these loops is similar to those in ordinary groups. In this way for the subclass of finitely generated commutative moufang loops we have a classification theorem of its approximate subloops." @default.
- W2605784693 created "2017-04-28" @default.
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- W2605784693 date "2016-12-20" @default.
- W2605784693 modified "2023-09-23" @default.
- W2605784693 title "Théorie des groupes approximatifs et ses applications" @default.
- W2605784693 hasPublicationYear "2016" @default.
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