[Cyclic groups of nonlinear transformations in morphology and the conception of cyclogenesis]

When describing multiunit organic forms, it is expedient to generalize the classic science on biological symmetries of similarity at the expense of transition to symmetry operations from wider groups of transformations, first of all mebiusian and projective. A vast class of biological structures is successfully modelled on the base of cyclic groups not only the linear, but also non-linear transformations. This is evidently connected with existence of morphogenetically significant biochemical cycles. The suggested means of mathematical modelling for biological symmetries open new possibilities of morphometrical analysis and investigation of a known problem of morphogenetic parallelisms. The results obtained prove V. V. Vernadsky's hypothesis on biological significance of the non-Euclidian geometry.