  This first part of the paper develops algebraic theory of linear anisotropic,
six-parametric nematic "N-operators" build up on the additive group of
traceless second rank 3D tensors. These operators have been implicitly used in
continual theories of nematic liquid crystals and weakly elastic nematic
elastomers. It is shown that there exists a noncommutative, multiplicative
group N6 of N-operators build up on a manifold in 6D space of parameters.
Positive N-operators, which in physical applications holds thermodynamic
stability constraints, form a subgroup of group N6 on a more complicated
manifold in parametric space. A three-parametric, commutative
transversal-isotropic subgroup S3 < N6 of positive symmetric nematic operators
is also briefly discussed. The special case of singular, non-negative symmetric
N-operators reveals the algebraic structure of nematic soft deformation modes.
