A New Class of Generalized Thompson's Groups and Their Normal Subgroups

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For a given group G and a homomorphism ϕ: G → G × G, we construct groups ℱϕ(G), 𝒯ϕ(G), and 𝒱ϕ(G) that blend Thompson's groups F, T, and V with G, respectively. Furthermore, we describe the lattice of normal subgroups of the groups ℱΔ(G), where Δ: G → G × G is the diagonal homomorphism, Δ(g) = (g, g).