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Non-linear electrodynamics arising in the frames of field theories innoncommutative space-time is examined on the base of quaternion formalism. Theproblem of form-invariance of the corresponding nonlinear constitutiverelations governed by six noncommutativity parameters $\theta_{kl}$ orquaternion \underline{K} = \underline{\theta} - i \underline{\epsilon} isexplored in detail. Two Abelian 2-parametric small groups, SO(2) \otimes O(1.1)or T_{2}, depending on invariant length \underline{K}^{2}\neq 0 or\underline{K}^{2}= 0 respectively, have been found. The way to interpret bothsmall groups in physical terms consists in factorizing corresponding Lorentztransformations into Euclidean rotations and Lorentzian boosts. In the contextof general study of various dual symmetries in noncommutative field theory, itis demonstrated explicitly that the nonlinear constitutive equations underconsideration are not invariant under continuous dual rotations, instead onlyinvariance under discrete dual transformation exists.

Quaternions and Small Lorentz Groups in Noncommutative Electrodynamics