This talk is about a joint work with Aris Papadopoulos and Blaise Boissonneau [BPT]. Starting from any first order structure S, Mekler constructs in [M] a 2-nilpotent group of prime exponent M=(G, ·) which interprets, in the pure language of groups, the structure S. This 2-nilpotent group shares numerous model theoretical properties with the structure S, notably in terms of dividing lines: M is Stable (resp. Simple, NIP_n for every n, Strong, NTP2...) if and only if S satisfies this property. See [CH]. I will motivate these results and show how one can generalise some of them, by considering a uniform hierarchy of dividing lines, introduced in [GHS]: the NC_K-hierarchy, which rises from coding (or not coding) Ramsey classes of structures K . I will also state a transfer principle for stably embedded pairs of Mekler groups (all these notions will be defined). Our method, that I will briefly sketch, was to establish new relative quantifier elimination results, and was inspired by a step-by-step approach for proving transfer principles in valued fields. [BPT] Boissonneau, Papadopoulos and T., Mekler's Construction and Murphy's Law for 2-Nilpotent Groups, arXiv:2403.20270. [GHS] Guingona, Hill and Scow, Characterizing model-theoretic dividing lines via collapse of generalized indiscernibles. [M] Mekler, Stability of nilpotent groups of class 2 and prime exponent. [CH] Chernikov and Hempel, Mekler's construction and generalized stability.